Single-cell perturbation response prediction method based on regulation reinforced discrete diffusion model

Abstract

The application discloses a single-cell perturbation response prediction method based on a regulation reinforcement discrete diffusion model. The method first trains a mask discrete diffusion generation model to predict the gene expression that is masked; a regulation strategy module is optimized through reinforcement learning to learn the optimal gene prediction sequence; and finally, the predicted expression profile after perturbation is output. The application converts the single-cell perturbation response prediction from the traditional single-step prediction into a gene-by-gene and multi-step generation process guided by the gene regulation relationship, so that the gene response that has been predicted can serve as context information for subsequent gene prediction, thereby more accurately simulating the propagation process of the perturbation effect in the gene regulation network. The application can improve the accuracy, stability and biological interpretability of single-cell perturbation response prediction, and can be applied to virtual cell modeling, functional genomics, drug screening, disease mechanism research and precision medicine scenarios.

Description

Technical Field

[0001] This invention belongs to the fields of artificial intelligence, bioinformatics, single-cell omics analysis and virtual cell modeling technology, and in particular relates to a single-cell perturbation response prediction method based on a regulation-enhanced discrete diffusion model. Background Technology

[0002] Cells are the basic functional units of life, and they exhibit complex molecular responses when influenced by gene editing, drug treatment, environmental stimuli, or disease-related factors. Accurately predicting cellular transcriptomic responses under specific perturbation conditions is crucial for understanding gene function, elucidating disease mechanisms, screening drug targets, and achieving personalized treatment.

[0003] In recent years, with the development of single-cell sequencing and high-throughput perturbation experiments, researchers have been able to measure cell expression states under different perturbation conditions at single-cell resolution. For example, techniques such as Perturb-seq, CRISPRi, and drug perturbation experiments can systematically collect cell expression profiles before and after perturbation, providing an important data foundation for constructing virtual cell models. Virtual cell models refer to models that simulate cell responses to different perturbations in a computer by learning the mapping relationship between cell state, perturbation conditions, and response results using artificial intelligence methods. These models can reduce the cost of wet experiments and provide computational assistance for functional genomics and drug development.

[0004] Existing methods for predicting single-cell perturbation responses can be broadly categorized into traditional single-step prediction methods, graph neural network-based methods, and diffusion model-based methods. Single-step prediction methods typically utilize architectures such as MLPs, Transformers, and variational autoencoders, directly mapping the control cell state and perturbation conditions to the final perturbed expression profile. Graph neural network-based methods often leverage relationships between genes to enhance expression representation. Diffusion model-based methods, on the other hand, gradually generate the perturbed expression state through a multi-step denoising process.

[0005] However, existing technologies still have the following shortcomings. First, traditional single-step prediction methods treat the perturbation response as a static endpoint, focusing only on the predicted result of the final expression profile while ignoring the gradual propagation of the perturbation effect in the gene regulatory network. In reality, cellular responses usually involve the continuous influence of upstream regulators on downstream target genes; the responses of different genes are not completely independent, nor do they occur simultaneously. Therefore, generating a complete expression profile directly through a single forward prediction is insufficient to fully reflect gene regulatory dependencies. Second, while existing diffusion-based methods have multi-step generation capabilities, their generation process typically performs global denoising at the entire expression profile level, without explicitly modeling the gene-level generation order of "which genes should be predicted first and which should be predicted later." This results in models that, while having an iterative generation form, lack clear biological regulatory significance in their generation trajectories. Third, existing models utilizing gene regulatory networks typically treat regulatory relationships as static priors to improve gene representation or information transmission, rather than to guide the expression profile generation process. In other words, while gene regulatory networks are used to enhance model inputs or internal features, they are rarely used to dynamically determine the generation order of gene responses, thus making it difficult to simulate regulatory cascade processes. Fourth, different perturbation conditions and cellular contexts may correspond to different gene regulatory relationships. Fixed regulatory priors cannot adapt to the regulatory differences under different perturbation conditions, which may lead to a decline in model performance when performing combined perturbations, cross-perturbation generalization, or cross-cell state generalization.

[0006] Therefore, there is an urgent need for a new single-cell perturbation response prediction method that can model the perturbation response as a gene-level stepwise generation process guided by regulatory relationships. This would enable the model to not only accurately predict the expression profile after perturbation, but also learn how to stepwise construct the perturbation response given a perturbation and cellular context, thereby improving prediction accuracy and biological interpretability. Summary of the Invention

[0007] In view of the above-mentioned shortcomings, this invention proposes a single-cell perturbation response prediction method based on a regulatory reinforcement discrete diffusion model to address the problems of existing single-cell perturbation response prediction methods, such as the lack of gene-level modeling of the perturbation response generation process, the failure of regulatory dependencies to effectively participate in the generation order decision, and the lack of biological interpretability of the generation trajectory. This method uses a masked discrete diffusion model to analyze the single-cell transcriptome expression state after generation perturbation and dynamically determines the generation order of gene expression using gene regulatory networks and reinforcement learning strategies, thereby achieving high-precision prediction of single-cell transcriptome responses under different perturbation conditions.

[0008] To achieve the above-mentioned objectives, the present invention specifically adopts the following technical solution:

[0009] In a first aspect, the present invention provides a method for predicting single-cell perturbation response based on a modulated enhanced discrete diffusion model, comprising the following steps:

[0010] S1. Obtain the perturbation response data of all genes in each single-cell sample. The perturbation response data of each gene includes the control expression profile, perturbation conditions, covariates, and continuous perturbation true expression profile. Discretize the perturbation true expression profile of each gene to form the corresponding discretized true expression profile.

[0011] S2. Train the masked discrete diffusion generation model. The training objective is to predict the discretized predicted expression profiles of the masked genes from the state where the discretized true expression profiles of a subset of genes are masked, given the control expression profile, perturbation conditions, and covariates.

[0012] S3. Perform cold-start training on the regulatory strategy module based on the gene regulation network; after cold-start training, fix the trained mask discrete diffusion generation model parameters and optimize the regulatory strategy module through reinforcement learning; during the optimization process, model the gene selection process of the regulatory strategy module as a trajectory decision process, and use the single-step prediction reward and the overall prediction reward to form the total reward of reinforcement learning, so that the regulatory strategy module learns the gene selection trajectory related to perturbation conditions and covariates.

[0013] S4. The reinforcement learning-trained regulatory strategy module and the trained masked discrete diffusion generation model are combined to form a regulatory reinforcement discrete diffusion model. The fully masked expression marker sequence with all gene positions as masked labels is used as input to the regulatory reinforcement discrete diffusion model. In each generation step, the regulatory strategy module calculates the decoding probability of genes with masked positions based on the currently generated expression marker sequence, perturbation conditions, covariates, and gene regulatory network. Based on the decoding probability, the gene set to be predicted in the current generation step is determined. The masked discrete diffusion generation model then predicts the discrete expression profile of each gene in the gene set and fills it into the currently generated expression marker sequence until all genes have been predicted. The discrete expression profile of all genes is converted into a perturbed predicted expression profile through the expression profile format conversion module to complete the single-cell perturbation response prediction.

[0014] Based on the above scheme, each step can be implemented in the following preferred manner.

[0015] As a preferred embodiment of the first aspect above, in S2, the internal data processing of the mask discrete diffusion generation model during training is as follows:

[0016] S21. Discretized true expression profiles of all genes Starting from this point, the diffusion time is randomly sampled, and according to a masking strategy, the discretized true expression profiles of a portion of the genes are replaced with masked markers to obtain the expression marker sequences in the masked state. In the masked state, each element in the expression marker sequence represents the expression value of a gene;

[0017] The masking strategy is: for the first... One gene, its diffusion time The expression value below With preset probability Keep the first Discrete true expression profile of each gene With probability Replaced with mask marker ;in, ;

[0018] S22. Masked Discrete Diffusion Generation Model: Representation of Label Sequences in Masked States As input, the control expression spectrum, perturbation conditions and covariates are first encoded by their respective linear encoders, and the encoded expression spectrum embedding, perturbation condition embedding and covariate embedding are concatenated to form a conditional representation;

[0019] S23. The masked expression marker sequence and each gene are passed through an embedding layer to obtain the expression marker embedding and gene identity embedding respectively. Then, the expression marker embedding, gene identity embedding and conditional representation are concatenated and input into the conditional denoising predictor. The Logits output by the conditional denoising predictor are converted into a probability distribution of the discretized predicted expression spectrum falling on the representative values ​​of each bin through Softmax. The bin representative value with the highest probability is selected from the probability distribution as the discretized predicted expression spectrum of the masked gene.

[0020] As a preferred embodiment of the first aspect mentioned above, in S2, the loss function used during training of the masked discrete diffusion generation model is the cross-entropy loss between the discretized predicted expression spectrum and the discretized true expression spectrum, and the parameters of the masked discrete diffusion generation model are updated based on minimizing this cross-entropy loss.

[0021] As a preferred embodiment of the first aspect above, in S3, the gene regulatory network As a biological a priori concept, it treats genes as nodes and the regulatory dependencies between genes as edges, represented as... Then, the current expression marker sequence, gene identity embedding, perturbation conditional embedding, and covariate embedding are concatenated and processed through an MLP to generate node features for each node in the gene regulatory network; among which, Represents a set of genes. This indicates the manipulation of the adjacency matrix, specifically the manipulation of its elements. Indicates the first One gene For the One gene The regulatory dependence relationship.

[0022] As a preferred embodiment of the first aspect above, in S3, the regulation strategy module takes the strategy state as input. The strategy state includes the expression marker sequence, perturbation conditions, covariates, and a candidate gene set. The candidate gene set consists of candidate genes whose expression values ​​are still masked. Then, the node features corresponding to each candidate gene are propagated on the gene regulation network through a graph attention network to obtain updated node features. The updated node features are mapped to the scores of each candidate gene selected for decoding under the strategy state through a multilayer perceptron. The scores of each candidate gene are then normalized by Softmax to the decoding probability of the candidate gene selected under the strategy state to predict its discretized predicted expression profile.

[0023] As a preferred embodiment of the first aspect mentioned above, in S3, the target probability of each gene being selected is obtained by using the reverse PageRank tool based on the regulatory dependence of each gene in the gene regulation network. This probability is used to represent the true priority of each gene when predicting the discretized expression profile. The cross-entropy loss between the decoding probability and the target probability output by the regulation strategy module is used as the cold start loss. The regulation strategy module is then trained by minimizing the cold start loss.

[0024] As a preferred approach to the first aspect mentioned above, in the reinforcement learning of S3, the regulatory strategy module starts from a fully masked expression marker sequence where the expression values ​​of all genes are masked, and begins multiple rounds of iteration. The specific processing flow for each round of iteration is as follows:

[0025] S31. In each iteration In this process, for each single-cell sample, the expression marker sequence generated in the current iteration is first used as the current expression marker sequence. And in conjunction with perturbation conditions, covariates, and the current candidate gene set. Together they constitute the current policy state. Then from the current strategy state Medium sampling A gene selection trajectory is formed by selecting candidate genes from the current candidate gene set to create a set of genes to be processed; For perturbation conditions; For covariates;

[0026] S32. For the first The gene selection trajectory is generated by the regulatory strategy module after cold start, which calculates the decoding probability of each candidate gene in the gene set to be processed and sorts them in descending order of decoding probability to form the target gene set. The trained masked discrete diffusion generation model predicts the target gene set based on the current expression marker sequence, removes the mask marker from the target gene set, and calculates the first... The single-step prediction reward and the overall prediction reward of the gene selection trajectory are used to obtain the first... The total reward for each gene selection trajectory;

[0027] S33. Calculate the relative advantage within a group for different gene selection trajectories, and use a strategy with a pruning function to optimize the parameters of the target update regulatory strategy module, thereby completing one round of iteration.

[0028] As a preferred embodiment of the first aspect mentioned above, in S32, the first... Single-step prediction reward for gene selection trajectory Overall prediction reward and total reward They are represented as follows:

[0029]

[0030]

[0031]

[0032] in, Indicate The average cross-entropy loss calculated above; For the first Expression marker sequences for gene selection trajectories; For the masked discrete diffusion generation model, given the current policy state and related conditions The conditional probability distribution of the output; , and All are weights, used to balance the three evaluation indicators: correlation coefficient, cosine similarity, and mean square error; To predict the change vector of the disturbance; This represents the actual perturbation change vector; for and The correlation coefficient between them; for and Cosine similarity between them; for and The mean square error between them; For the first Predicted expression profiles after perturbation of gene selection trajectories; The true representation spectrum after perturbation; For comparison expression profiles; This indicates the weight of the overall predicted reward.

[0033] As a preferred embodiment of the first aspect mentioned above, the specific method for obtaining the perturbed predicted expression spectrum through the expression spectrum format conversion module is as follows: based on the bin representative value corresponding to the discretized predicted expression spectrum of the gene, the discretized predicted expression spectrum is dequantized into a continuous original expression spectrum, and then the continuous original expression spectrum, perturbation conditions, and covariates are passed through a multilayer perceptron to output the perturbed predicted expression spectrum.

[0034] In a second aspect, the present invention provides a single-cell perturbation response prediction system based on a modulated enhanced discrete diffusion model, for implementing the single-cell perturbation response prediction method based on a modulated enhanced discrete diffusion model as described in any of the embodiments of the first aspect above.

[0035] Thirdly, the present invention provides a computer program product, including a computer program / instruction, which, when executed by a processor, can realize the single-cell perturbation response prediction method based on the modulated enhanced discrete diffusion model as described in any of the solutions of the first aspect above.

[0036] Fourthly, the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the single-cell perturbation response prediction method based on the modulated enhanced discrete diffusion model as described in any of the embodiments of the first aspect above.

[0037] Fifthly, the present invention provides a computer electronic device, which includes a memory and a processor;

[0038] The memory is used to store computer programs;

[0039] The processor is configured to, when executing the computer program, implement the single-cell perturbation response prediction method based on the modulated enhanced discrete diffusion model as described in any of the above-described first aspects.

[0040] Compared with the prior art, the present invention has the following advantages:

[0041] First, this invention models single-cell perturbation response prediction as a stepwise gene-level generation process, rather than outputting a complete expression profile all at once. In this way, the generated gene expression responses can serve as explicit context for subsequent gene predictions, thereby better modeling the dependencies between gene expressions.

[0042] Second, this invention uses gene regulatory networks to guide the generation sequence, rather than simply to enhance gene representation. This design allows biological regulatory priors to directly participate in the perturbation response construction process, giving the generation trajectory a more explicit biological meaning.

[0043] Third, this invention optimizes the generation strategy by regulating known reinforcement learning, enabling the model to learn different gene generation pathways for different perturbation conditions and cell contexts, thereby improving the model's adaptability to complex perturbations, combined perturbations, and different cell states.

[0044] Fourth, this invention employs both single-step prediction rewards and overall prediction rewards, enabling the control strategy to focus not only on the prediction accuracy of the current step, but also on the consistency between the final disturbance response and the actual response, thereby improving the overall prediction quality.

[0045] Fifth, this invention adopts a combination of discrete expression marker generation and continuous expression calibration. It uses a masked discrete diffusion model to improve generation stability and restores fine-grained changes in expression values ​​through an expression spectrum format conversion module, thus balancing the stability of the generation process and the accuracy of the final expression prediction. Attached Figure Description

[0046] Figure 1 The flowchart of this invention

[0047] Figure 2 This is a comparison chart of the gene expression perturbation response prediction performance of the present invention and existing methods on the Norman dataset.

[0048] Figure 3 This is a system block diagram of the present invention;

[0049] Figure 4 This is a schematic diagram of a computer electronic device provided by the present invention. Detailed Implementation

[0050] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of the present invention. However, the present invention can be practiced in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below. Technical features in the various embodiments of the present invention can be combined accordingly without mutual conflict.

[0051] In the description of this invention, it should be understood that the terms "first" and "second" are used only for descriptive purposes and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Therefore, a feature defined with "first" and "second" may explicitly or implicitly include at least one of those features.

[0052] Based on the above background technology, in order to solve the problems that existing single-cell perturbation response prediction methods are difficult to model gene regulation cascade processes, lack regulatory relationship guidance in the generation process, and have insufficient prediction accuracy under complex perturbation conditions, this invention provides a single-cell perturbation response prediction method based on a regulation-enhanced discrete diffusion model.

[0053] like Figure 1 As shown, in a preferred embodiment of the present invention, the single-cell perturbation response prediction method based on the modulated enhanced discrete diffusion model includes the following steps S1 to S4. The specific implementation process of each step is described in detail below.

[0054] S1. Obtain the perturbation response data of all genes in each single-cell sample. The perturbation response data of each gene includes the control expression profile, perturbation conditions, covariates, and continuous perturbation true expression profile. Discretize the perturbation true expression profile of each gene to form the corresponding discretized true expression profile.

[0055] It should be noted that in step S1 of this invention, the gene set is assumed to be... ,in, Indicates the number of genes. Indicates the first One gene, For each single-cell sample, perturbation response data for all genes included control expression profiles. Disturbance conditions Covariates True expression spectrum after perturbation Among them, the control expression profile is used to represent the gene expression state of cells when they are not affected by the target perturbation; the perturbation condition is used to represent gene overexpression, gene knockdown, CRISPRi intervention, drug treatment or other perturbations applied to cells; the covariate is used to represent cell type, batch, experimental conditions, developmental stage or other contextual information; and the perturbation-based true expression profile is used as a supervision signal for model training.

[0056] It should be noted that, in step S1 of this invention, after obtaining the required perturbation response data, the specific method for discretizing the true expression spectrum after perturbation is as follows: using an equal-frequency binning operator. , will the True expression profile of each gene after perturbation Mapped to One of the values ​​represented by each sub-bin is used to obtain the first... Discrete true expression profile of each gene Thus obtain Discrete true expression profile of each gene .in, This represents the quantity of the bins.

[0057] Furthermore, in this embodiment, the above discretization method can employ equal-frequency binning, or, depending on the actual application requirements, equal-width binning, adaptive binning based on expression distribution, or learnable quantization. Equal-frequency binning enables different expression intervals to contain a relatively balanced number of samples, thereby alleviating the high sparsity and skewed distribution problems existing in single-cell expression data.

[0058] S2. Train the masked discrete diffusion generation model. The training objective is to predict the discretized predicted expression profiles of the masked genes from the state where the discretized true expression profiles of a subset of genes are masked, given the control expression profile, perturbation conditions, and covariates.

[0059] It should be noted that, in step S2, the internal data processing of the mask discrete diffusion generation model during training is as follows:

[0060] S21. Discretized true expression profiles of all genes Starting from this point, the diffusion time is randomly sampled, and according to a masking strategy, the discretized true expression profiles of a portion of the genes are replaced with masked markers to obtain the expression marker sequences in the masked state. In the masked state, each element in the expression marker sequence represents the expression value of a gene.

[0061] Furthermore, in step S21, the masking strategy is as follows: for the first... One gene, its diffusion time The expression value below With preset probability Keep the first Discrete true expression profile of each gene With probability Replaced with mask marker ;in, .

[0062] Therefore, the expression tag sequence in the masked state In this context, the expression value of a gene could be either the discretized true expression profile of that gene, or a masked representation of its discretized true expression profile. This masking process can be represented as:

[0063]

[0064] in, Given a discretized true representation spectrum At that time, the diffusion time was Expression tag sequence in time mask state The conditional probability distribution; For probability vectors The categorical distribution of the parameters represents according to The given probability values; To concentrate on Unit point mass distribution on; To focus on the mask mark The mass distribution at a unit point on the surface.

[0065] S22. Masked Discrete Diffusion Generation Model: Representation of Label Sequences in Masked States As input, the control expression spectrum, perturbation conditions, and covariates are first encoded by their respective linear encoders. The encoded expression spectrum embedding, perturbation condition embedding, and covariate embedding are then concatenated to form a conditional representation.

[0066] Further, in step S22, the linear encoder corresponding to the expression spectrum is denoted as... The corresponding expression profile embedding is denoted as The linear encoder corresponding to the disturbance condition is denoted as . The corresponding perturbation condition embedding is denoted as The linear encoder corresponding to the covariate is denoted as . The corresponding covariate embedding is denoted as The conditional representation obtained after concatenating the three embeddings is denoted as follows: .

[0067] S23. The masked expression marker sequence and each gene are passed through an embedding layer to obtain the expression marker embedding and gene identity embedding respectively. Then, the expression marker embedding, gene identity embedding and conditional representation are concatenated and input into the conditional denoising predictor. The Logits output by the conditional denoising predictor are converted into a probability distribution of the discretized predicted expression spectrum falling on the representative values ​​of each bin through Softmax. The bin representative value with the highest probability is selected from the probability distribution as the discretized predicted expression spectrum of the masked gene.

[0068] Furthermore, in step S23, the conditional denoising predictor employs a non-causal Transformer.

[0069] It should be noted that in step S2 of this invention, the loss function used by the masked discrete diffusion generation model during training is the cross-entropy loss between the discretized predicted expression spectrum and the discretized true expression spectrum, and the parameters of the masked discrete diffusion generation model are updated based on minimizing this cross-entropy loss.

[0070] In this embodiment, when training the masked discrete diffusion generation model, the cross-entropy loss is calculated only for the masked gene locations, and not for the gene locations that are not masked (i.e., the discretized true expression profile is already visible). In this way, the masked discrete diffusion generation model can learn how to infer the discretized predicted expression profile that has not yet been generated based on the control expression profile, perturbation conditions, covariates, and the known discretized true expression profile.

[0071] The above cross-entropy loss Represented as:

[0072]

[0073] in, Generate model parameters for mask discrete diffusion; To achieve the desired outcome; diffusion time The set of mask markers below; The probability distribution of the output of the mask discrete diffusion generation model.

[0074] S3. Perform cold-start training on the regulatory strategy module based on the gene regulation network; after cold-start training, fix the trained mask discrete diffusion generation model parameters and optimize the regulatory strategy module through reinforcement learning; during the optimization process, model the gene selection process of the regulatory strategy module as a trajectory decision process, and use the single-step prediction reward and the overall prediction reward to form the total reward of reinforcement learning, so that the regulatory strategy module learns the gene selection trajectory related to perturbation conditions and covariates.

[0075] It should be noted that in step S3 of this invention, the gene regulatory network... As a biological a priori concept, it treats genes as nodes and the regulatory dependencies between genes as edges, represented as... Then, the current expression marker sequence, gene identity embedding, perturbation conditional embedding, and covariate embedding are concatenated and processed through an MLP to generate node features for each node in the gene regulatory network; among which, Represents a set of genes. This indicates the manipulation of the adjacency matrix, specifically the manipulation of its elements. Indicates the first One gene For the One gene The regulatory dependence relationship.

[0076] In this embodiment, the regulatory adjacency matrix can be derived from existing biological prior knowledge, experimental databases, inferred gene regulatory networks, or regulatory dependencies learned from single-cell samples.

[0077] It should be noted that in step S3 of this invention, in order to make the generation order of gene expression profile conform to the potential regulatory relationship, this invention further constructs a regulatory strategy module based on the above-mentioned gene regulatory network.

[0078] Specifically, the regulatory strategy module takes the strategy state as input, which includes the expression marker sequence, perturbation conditions, covariates, and a set of candidate genes. The candidate gene set consists of candidate genes whose expression values ​​are still masked. Then, the node features corresponding to each candidate gene are propagated across the gene regulation network using a Graph Attention Network (GAT) to obtain updated node features, which are then processed by a multilayer perceptron. The updated node features are mapped to the selection of candidate genes under this strategy state. The scores are decoded, and the scores of each candidate gene are normalized using Softmax to determine the candidate gene selection under the policy state. Predict the decoding probability of its discretized predictive expression spectrum .

[0079] With the first Candidate genes For example, its corresponding decoding probability Represented as:

[0080]

[0081] in, For the first The score of each candidate gene; For the first Updated node features corresponding to each candidate gene; This represents the temperature parameter.

[0082] Furthermore, to avoid the regulatory strategy module exploring completely randomly in the early stages of reinforcement learning, this embodiment first utilizes gene regulation priors for cold-start training. Specifically, based on the regulatory dependencies of each gene in the gene regulation network, the inverse PageRank tool is used to obtain the target probability of each gene being selected. This is used to represent the true priority of each gene when predicting the discretized expression profile; and the cross-entropy loss between the decoded probability and the target probability output by the regulatory strategy module is used as the cold start loss. The control strategy module is trained by minimizing the cold start loss:

[0083]

[0084] in, These are the parameters for the control strategy module.

[0085] After cold start training, the regulatory strategy module can preferentially select upstream regulatory genes, thereby enabling the masked discrete diffusion generation model to predict the discrete expression profile of the gene, providing an initial strategy that conforms to biological priors for subsequent reinforcement learning optimization.

[0086] It should be noted that, in step S3 of this invention, after the masked discrete diffusion generation model has been trained, its parameters are fixed, and the gene prediction order is further optimized by optimizing only the parameters of the regulatory strategy module. This setting decouples the discretized expression profile prediction capability from the prediction order optimization capability: the masked discrete diffusion generation model is responsible for predicting the discretized expression profile of the selected genes, while the regulatory strategy module is responsible for deciding which genes to select for prediction at each step.

[0087] In reinforcement learning, the regulatory strategy module starts from a fully masked expression marker sequence where the expression values ​​of all genes are masked, and begins multiple iterations. The specific processing flow of each iteration is as follows:

[0088] S31. In each iteration In the process, for each single-cell sample First, the expression label sequence generated in the current iteration is used as the current expression label sequence. And in conjunction with perturbation conditions, covariates, and the current candidate gene set. Together they constitute the current policy state. Then from the current strategy state Medium sampling A gene selection trajectory is formed by selecting candidate genes from the current candidate gene set to create a set of genes to be processed.

[0089] It should be noted that in embodiment S31 of this invention, assuming that the current candidate gene set contains 50 genes, the gene set to be processed contains 20 genes, which can be understood as a subset of genes sampled from the 50 genes. Therefore, these 20 genes are the same for each gene selection trajectory. For each gene selection trajectory, the regulatory strategy module will sort these 20 genes according to the trajectory. Thus, the masked discrete diffusion generation model can subsequently predict the gene order for each trajectory.

[0090] S32. For the first The gene selection trajectory is generated by the regulatory strategy module after cold start, which calculates the decoding probability of each candidate gene in the gene set to be processed and sorts them in descending order of decoding probability to form the target gene set. The trained masked discrete diffusion generation model predicts the target gene set based on the current expression marker sequence, removes the mask marker from the target gene set, and calculates the first... The single-step prediction reward and the overall prediction reward of the gene selection trajectory are used to obtain the first... The total reward for each gene selection trajectory.

[0091] Furthermore, in S32, the first Single-step prediction reward for gene selection trajectory Represented as:

[0092]

[0093] in, Indicate The average cross-entropy loss calculated above; For the first Expression marker sequences for gene selection trajectories; For the masked discrete diffusion generation model, given the current policy state and related conditions The conditional probability distribution of the output.

[0094] Furthermore, in S32, the first Overall prediction reward for gene selection trajectories Represented as:

[0095]

[0096]

[0097]

[0098] in, , and All are weights, used to balance the three evaluation indicators: correlation coefficient, cosine similarity, and mean square error; To predict the change vector of the disturbance; This represents the actual perturbation change vector; for and The correlation coefficient between them; for and Cosine similarity between them; for and The mean square error between them; For the first Predicted expression profiles after perturbation of gene selection trajectories; The true representation spectrum after perturbation; This is a control expression profile.

[0099] Furthermore, the perturbation-predicted expression profile is still obtained through the expression profile format conversion module. Specifically, the conversion method is as follows: based on the bin representative value corresponding to the discretized predicted expression profile of the gene, the discretized predicted expression profile is dequantized into a continuous raw expression profile. Then, the continuous raw expression profile, perturbation conditions, and covariates are passed through a multilayer perceptron to output the perturbation-predicted expression profile.

[0100] In this embodiment, since discrete binning results in the loss of fine-grained variations within the discretized predicted expression spectrum, after obtaining the discretized predicted expression spectrum generated by the masked discrete diffusion model, it needs to be further converted into a perturbed predicted expression spectrum. The specific process is as described above and will not be repeated here. It should be noted that the lightweight multilayer perceptron that outputs the perturbed predicted expression spectrum is trained using a continuous reconstruction loss between the perturbed predicted expression spectrum and the perturbed true expression spectrum. By reconstructing the discretized predicted expression spectrum into a perturbed predicted expression spectrum, this invention can restore the fine-grained variations of continuous expression values ​​while maintaining the stability of discrete generation.

[0101] Furthermore, in S32, the first Total reward of gene selection trajectory Represented as:

[0102]

[0103] in, This indicates the weight of the overall predicted reward.

[0104] It should be noted that in embodiment S32 of this invention, by combining single-step prediction rewards and overall prediction rewards, the regulatory strategy module not only learns which genes are easily predicted accurately in the current iteration, but also learns which gene priority generation can improve the prediction quality of the perturbation-predicted expression profile. The single-step prediction reward measures the prediction quality of the discretized predicted expression profile on the selected gene set in the current iteration. If the genes selected by the regulatory strategy module can be accurately predicted based on the current context, the corresponding average cross-entropy loss is low, and the single-step prediction reward is high. The overall prediction reward is used to measure the consistency between the perturbation-based true expression profile and the perturbation-based predicted expression profile. The overall prediction reward uses three indicators: correlation coefficient, cosine similarity, and mean squared error of the perturbation change vector. Higher correlation coefficients and cosine similarities indicate that the regulatory strategy module is better at capturing the perturbation direction; lower mean squared errors indicate that the regulatory strategy module is better at accurately recovering expression values.

[0105] S33. Calculate the relative advantage within a group for different gene selection trajectories, and use a strategy with a pruning function to optimize the parameters of the target update regulatory strategy module, thereby completing one round of iteration.

[0106] It should be noted that in embodiment S33 of this invention, the K gene selection trajectories obtained from the same single-cell sample are considered as a trajectory group. Since different gene selection trajectories under the same single-cell sample have the same input conditions, their total reward differences mainly come from different gene generation sequences. Therefore, the superiority or inferiority of different gene generation sequences can be evaluated by comparing the relative advantages within the group. The above-mentioned method for calculating the relative advantages within the group is prior art, and is briefly described in this embodiment as follows.

[0107] For the Total reward of gene selection trajectory Calculate the mean within the same trajectory group. and standard deviation ,right Normalize to obtain the first Intragroup relative dominance of gene selection trajectories :

[0108]

[0109]

[0110] in, To prevent stable terms with a denominator of zero; The number of trajectory selections for genes.

[0111] As can be seen from the above formula, if the first... If a gene selection trajectory has a higher total reward within the same trajectory group, its relative advantage within the group is positive, indicating that the gene selection strategy in that trajectory is more conducive to prediction; conversely, if the total reward is lower, its relative advantage within the group is negative.

[0112] In embodiment S33 of the present invention, the strategy optimization objective with a pruning function is... The calculation method belongs to the prior art, specifically:

[0113]

[0114] in, Indicates the proportion of the strategy; This is the clipping function; This indicates the clipping threshold.

[0115] S4. The reinforcement learning-trained regulatory strategy module and the trained masked discrete diffusion generation model are combined to form a regulatory reinforcement discrete diffusion model. The fully masked expression marker sequence with all gene positions as masked labels is used as input to the regulatory reinforcement discrete diffusion model. In each generation step, the regulatory strategy module calculates the decoding probability of genes with masked positions based on the currently generated expression marker sequence, perturbation conditions, covariates, and gene regulatory network. Based on the decoding probability, the gene set to be predicted in the current generation step is determined. The masked discrete diffusion generation model then predicts the discrete expression profile of each gene in the gene set and fills it into the currently generated expression marker sequence until all genes have been predicted. The discrete expression profile of all genes is converted into a perturbed predicted expression profile through the expression profile format conversion module to complete the single-cell perturbation response prediction.

[0116] It should be noted that in step S4 of this invention, when the enhanced discrete diffusion model is used for actual prediction, it takes a fully masked expression marker sequence with all gene positions as masked markers as input. The decoding probability of these masked genes is calculated by the regulatory strategy module as the priority representing the gene generation order. That is, the decoding probability is positively correlated with the priority of gene selection. Then, the genes to be predicted next can be selected according to this priority, so that high-priority genes are predicted first and low-priority genes are predicted later. With the help of the predictive ability of the masked discrete diffusion generation model, the discrete predicted expression profiles of these masked genes are gradually predicted. In this way, the regulatory strategy module can dynamically adjust the gene generation order under different perturbations and different cellular contexts. For example, for a certain perturbation condition, the current expression marker sequence can preferentially generate upstream regulatory genes or key genes strongly correlated with the perturbation, so that their expression values ​​can be used as contextual information for subsequent downstream gene prediction.

[0117] Specifically, for each generation step Current expression marker sequence In this study, the expression values ​​at predicted gene locations are the discretized predicted expression profiles, while the expression values ​​at gene locations not yet predicted remain as masked labels. Therefore, this invention uses these masked expression values ​​as candidate genes and constructs a candidate gene set: , For the first Candidate genes The expression value, The candidate gene index is generated by the regulatory strategy module, which first obtains the decoding probabilities of these candidate genes and selects the candidate gene with the highest decoding probability. Then, a trained masked discrete diffusion generation model is invoked to predict the discretized expression profile of the selected candidate gene. After each prediction, the mask marker at the selected candidate gene position is replaced with the predicted discretized expression profile, thus updating the current expression marker sequence. Furthermore, the selected candidate gene is excluded from the candidate gene set. The discretized expression profiles of genes that have already been predicted remain fixed in subsequent steps and participate in the prediction of subsequent genes as contextual information. This process iterates until the discretized expression profiles of all genes have been predicted. Compared to random masking, the sequential generation of discretized expression profiles guided by the regulatory strategy module of this invention prioritizes genes with greater regulatory significance or those more helpful for subsequent predictions, thereby providing more effective contextual information for downstream gene response prediction.

[0118] On the Norman dataset, this invention predicts gene expression responses in K562 cells under 287 perturbation conditions. Pearson Δ is used to measure the consistency between the predicted results and the actual perturbation-induced expression changes; a higher value indicates a more accurate prediction. Figure 2 The results show that the Pearson Δ distribution of this invention is significantly superior to existing methods such as Squidiff, scDFM, Biolord, STATE, Cell Flow, and SAMS-VAE. This demonstrates that this invention can stably and accurately predict perturbation-induced gene expression changes. Compared to existing single-step prediction methods, this invention transforms perturbation response prediction into a multi-step gene generation process, utilizing the preferentially generated discrete predicted expression profiles as contextual information for subsequent gene predictions, thereby improving the model's ability to express complex perturbation responses. Compared to existing global denoising diffusion models, this invention employs a masked discrete diffusion method to progressively generate discrete predicted expression profiles in the gene-level expression marker space and explicitly models the generation order of different genes, making the prediction process more consistent with the biological mechanism of gradual propagation of gene regulatory signals. Compared to models that only treat gene regulatory networks as static features, this invention uses gene regulatory relationships to guide the gene selection trajectory itself, directly determining which genes will be preferentially generated, thereby enhancing the model's biological interpretability. Compared with methods that use a fixed or random generation order, this invention enables the model to dynamically form generation paths for different perturbation conditions and cellular contexts by regulating a known reinforcement learning optimization strategy, thereby improving its adaptability to different perturbation types and biological situations.

[0119] It should also be noted that the single-cell perturbation response prediction method based on the modulated enhanced discrete diffusion model in the above embodiments can essentially be executed by a computer program or module. Therefore, similarly, based on the same inventive concept, another preferred embodiment of the present invention also provides a single-cell perturbation response prediction system based on the modulated enhanced discrete diffusion model, corresponding to the single-cell perturbation response prediction method based on the modulated enhanced discrete diffusion model provided in the above embodiments, such as... Figure 3 As shown, it includes:

[0120] The data acquisition module is used to acquire the perturbation response data of all genes in each single-cell sample. The perturbation response data of each gene includes the control expression profile, perturbation conditions, covariates, and continuous perturbation true expression profile. The perturbation true expression profile of each gene is discretized to form the corresponding discretized true expression profile.

[0121] The model training module is used to train the masked discrete diffusion generation model. The training objective is to enable the masked discrete diffusion generation model to predict the discretized true expression profiles of a subset of genes under the given conditions of control expression profiles, perturbation conditions, and covariates, and output the discretized predicted expression profiles of the masked genes.

[0122] The reinforcement learning optimization module is used for cold-start training of the gene regulation strategy module based on the gene regulation network. After cold-start training, the trained mask discrete diffusion generation model parameters are fixed, and the regulation strategy module is optimized through reinforcement learning. During the optimization process, the gene selection process of the regulation strategy module is modeled as a trajectory decision process. The total reward of reinforcement learning is composed of single-step prediction reward and overall prediction reward, so that the regulation strategy module learns the gene selection trajectory related to perturbation conditions and covariates.

[0123] The prediction module combines the reinforcement learning-learned regulatory strategy module with the trained masked discrete diffusion generation model to form a regulatory reinforcement discrete diffusion model. The fully masked expression marker sequence, where all gene positions are masked, is used as input to the regulatory reinforcement discrete diffusion model. In each generation step, the regulatory strategy module calculates the decoding probability of genes whose gene positions are still masked based on the currently generated expression marker sequence, perturbation conditions, covariates, and the gene regulatory network. Based on this decoding probability, it determines the set of genes to be predicted in the current generation step. The masked discrete diffusion generation model then predicts the discrete expression profiles of each gene in the gene set and fills them into the currently generated expression marker sequence. This process continues until all genes have been predicted. Finally, the discrete expression profiles of all genes are converted into perturbed predicted expression profiles through the expression profile format conversion module, completing the single-cell perturbation response prediction.

[0124] It is understood that the single-cell perturbation response prediction method based on the modulated enhanced discrete diffusion model described in S1-S4 above can essentially be implemented by a computer program. Therefore, based on the same inventive concept, another preferred embodiment of the present invention also provides a computer program product corresponding to the single-cell perturbation response prediction method based on the modulated enhanced discrete diffusion model provided in the above embodiments. This product includes a computer program / instruction, which, when executed by a processor, can implement the single-cell perturbation response prediction method based on the modulated enhanced discrete diffusion model as described in the above embodiments.

[0125] Similarly, based on the same inventive concept, another preferred embodiment of the present invention also provides a computer electronic device corresponding to the single-cell perturbation response prediction method based on the regulated enhanced discrete diffusion model provided in the above embodiments, such as... Figure 4 As shown, it includes a memory and a processor;

[0126] The memory is used to store computer programs;

[0127] The processor is configured to, when executing the computer program, implement the single-cell perturbation response prediction method based on the modulated enhanced discrete diffusion model in the above embodiments.

[0128] Furthermore, the logical instructions in the aforementioned memory can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention.

[0129] Therefore, based on the same inventive concept, another preferred embodiment of the present invention also provides a computer-readable storage medium corresponding to the single-cell perturbation response prediction method based on the modulated enhanced discrete diffusion model provided in the above embodiments. The storage medium stores a computer program, which, when executed by a processor, can realize the single-cell perturbation response prediction method based on the modulated enhanced discrete diffusion model in the above embodiments.

[0130] Specifically, in the computer-readable storage medium of the above three embodiments, the stored computer program is executed by a processor, which can perform the aforementioned steps S1 to S4.

[0131] It is understood that the aforementioned storage media may include random access memory (RAM) or non-volatile memory (NVM), such as at least one disk storage device. Furthermore, the storage media may also be various media capable of storing program code, such as USB flash drives, external hard drives, magnetic disks, or optical discs.

[0132] It is understood that the processors mentioned above can be general-purpose processors, including central processing units (CPUs), network processors (NPs), etc.; they can also be digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.

[0133] It should also be noted that those skilled in the art will understand that, for the sake of convenience and brevity, the specific working process of the system described above can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here. In the embodiments provided in this application, the division of steps or modules in the system and method is merely a logical functional division, and there may be other division methods in actual implementation. For example, multiple modules or steps may be combined or integrated together, and a module or step may also be split.

[0134] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the invention. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the invention. Therefore, all technical solutions obtained through equivalent substitution or transformation fall within the protection scope of the present invention.

Claims

1. A method for predicting single-cell perturbation response based on a modulated enhanced discrete diffusion model, characterized in that, Includes the following steps: S1. Obtain the perturbation response data of all genes in each single-cell sample. The perturbation response data of each gene includes the control expression profile, perturbation conditions, covariates, and continuous perturbation true expression profile. Discretize the perturbation true expression profile of each gene to form the corresponding discretized true expression profile. S2. Train the masked discrete diffusion generation model. The training objective is to predict the discretized predicted expression profiles of the masked genes from the state where the discretized true expression profiles of a subset of genes are masked, given the control expression profile, perturbation conditions, and covariates. S3. Perform cold-start training on the regulatory strategy module based on the gene regulation network; after cold-start training, fix the trained mask discrete diffusion generation model parameters and optimize the regulatory strategy module through reinforcement learning; during the optimization process, model the gene selection process of the regulatory strategy module as a trajectory decision process, and use the single-step prediction reward and the overall prediction reward to form the total reward of reinforcement learning, so that the regulatory strategy module learns the gene selection trajectory related to perturbation conditions and covariates. S4. The reinforcement learning-trained regulatory strategy module and the trained masked discrete diffusion generation model are combined to form a regulatory reinforcement discrete diffusion model. The fully masked expression marker sequence with all gene positions as masked labels is used as input to the regulatory reinforcement discrete diffusion model. In each generation step, the regulatory strategy module calculates the decoding probability of genes with masked positions based on the currently generated expression marker sequence, perturbation conditions, covariates, and gene regulatory network. Based on the decoding probability, the gene set to be predicted in the current generation step is determined. The masked discrete diffusion generation model then predicts the discrete expression profile of each gene in the gene set and fills it into the currently generated expression marker sequence until all genes have been predicted. The discrete expression profile of all genes is converted into a perturbed predicted expression profile through the expression profile format conversion module to complete the single-cell perturbation response prediction.

2. The single-cell perturbation response prediction method based on the modulated enhanced discrete diffusion model as described in claim 1, characterized in that, In S2, the internal data processing of the masked discrete diffusion generation model during training is as follows: S21. Discretized true expression profiles of all genes Starting from this point, the diffusion time is randomly sampled, and according to a masking strategy, the discretized true expression profiles of a portion of the genes are replaced with masked markers to obtain the expression marker sequences in the masked state. In the masked state, each element in the expression marker sequence represents the expression value of a gene; The masking strategy is: for the th One gene, its diffusion time The expression value below With preset probability Keep the first Discrete true expression profile of each gene With probability Replaced with mask marker ;in, ; S22. Masked Discrete Diffusion Generation Model: Representation of Label Sequences in Masked States As input, the control expression spectrum, perturbation conditions and covariates are first encoded by their respective linear encoders, and the encoded expression spectrum embedding, perturbation condition embedding and covariate embedding are concatenated to form a conditional representation; S23. The masked expression marker sequence and each gene are passed through an embedding layer to obtain the expression marker embedding and gene identity embedding respectively. Then, the expression marker embedding, gene identity embedding and conditional representation are concatenated and input into the conditional denoising predictor. The Logits output by the conditional denoising predictor are converted into a probability distribution of the discretized predicted expression spectrum falling on the representative values ​​of each bin through Softmax. The bin representative value with the highest probability is selected from the probability distribution as the discretized predicted expression spectrum of the masked gene.

3. The single-cell perturbation response prediction method based on the modulated enhanced discrete diffusion model as described in claim 2, characterized in that, In S2, the loss function used during training of the masked discrete diffusion generation model is the cross-entropy loss between the discretized predicted expression spectrum and the discretized true expression spectrum. The parameters of the masked discrete diffusion generation model are updated based on minimizing this cross-entropy loss.

4. The single-cell perturbation response prediction method based on the modulated enhanced discrete diffusion model as described in claim 2, characterized in that, In S3, the gene regulatory network As a biological a priori concept, it treats genes as nodes and the regulatory dependencies between genes as edges, represented as... Then, the current expression marker sequence, gene identity embedding, perturbation conditional embedding, and covariate embedding are concatenated and processed through an MLP to generate node features for each node in the gene regulatory network; among which, Represents a set of genes. This indicates the manipulation of the adjacency matrix, specifically the manipulation of its elements. Indicates the first One gene For the One gene The regulatory dependence relationship.

5. The single-cell perturbation response prediction method based on the modulated enhanced discrete diffusion model as described in claim 4, characterized in that, In S3, the regulation strategy module takes the strategy state as input. The strategy state includes the expression marker sequence, perturbation conditions, covariates, and a candidate gene set. The candidate gene set consists of candidate genes whose expression values ​​are still masked. Then, the node features corresponding to each candidate gene are propagated on the gene regulation network through a graph attention network to obtain updated node features. The updated node features are mapped to the scores of each candidate gene selected for decoding under the strategy state through a multilayer perceptron. The scores of each candidate gene are then normalized by Softmax to the decoding probability of the candidate gene selected under the strategy state to predict its discretized predicted expression profile.

6. The single-cell perturbation response prediction method based on the modulated enhanced discrete diffusion model as described in claim 5, characterized in that, In S3, based on the regulatory dependencies of each gene in the gene regulation network, the reverse PageRank tool is used to obtain the target probability of each gene being selected, which is used to represent the true priority of each gene when predicting the discretized expression profile. The cross-entropy loss between the decoding probability and the target probability output by the regulation strategy module is used as the cold start loss. The regulation strategy module is then trained by minimizing the cold start loss.

7. The single-cell perturbation response prediction method based on the modulated enhanced discrete diffusion model as described in claim 5, characterized in that, In S3's reinforcement learning, the regulatory strategy module starts from a fully masked expression marker sequence where the expression values ​​of all genes are masked, and begins multiple iterations. The specific processing flow for each iteration is as follows: S31. In each iteration In this process, for each single-cell sample, the expression marker sequence generated in the current iteration is first used as the current expression marker sequence. And in conjunction with perturbation conditions, covariates, and the current candidate gene set. Together they constitute the current policy state. Then from the current strategy state Medium sampling A gene selection trajectory is formed by selecting candidate genes from the current candidate gene set to create a set of genes to be processed; For perturbation conditions; For covariates; S32. For the first The gene selection trajectory is generated by the regulatory strategy module after cold start, which calculates the decoding probability of each candidate gene in the gene set to be processed and sorts them in descending order of decoding probability to form the target gene set. The trained masked discrete diffusion generation model predicts the target gene set based on the current expression marker sequence, removes the mask marker from the target gene set, and calculates the first... The single-step prediction reward and the overall prediction reward of the gene selection trajectory are used to obtain the first... The total reward for each gene selection trajectory; S33. Calculate the relative advantage within a group for different gene selection trajectories, and use a strategy with a pruning function to optimize the parameters of the target update regulatory strategy module, thereby completing one round of iteration.

8. The single-cell perturbation response prediction method based on the modulated enhanced discrete diffusion model as described in claim 7, characterized in that, In S32, the first Single-step prediction reward for gene selection trajectory Overall prediction reward and total reward They are represented as follows: ； ； ； in, Indicate The average cross-entropy loss calculated above; For the first Expression marker sequences for gene selection trajectories; For the masked discrete diffusion generation model, given the current policy state and related conditions The conditional probability distribution of the output; , and All are weights, used to balance the three evaluation indicators: correlation coefficient, cosine similarity, and mean square error; To predict the change vector of the disturbance; This represents the actual perturbation change vector; for and The correlation coefficient between them; for and Cosine similarity between them; for and The mean square error between them; For the first Predicted expression profiles after perturbation of gene selection trajectories; The true representation spectrum after perturbation; For comparison of expression profiles; This indicates the weight of the overall predicted reward.

9. The single-cell perturbation response prediction method based on the modulated enhanced discrete diffusion model as described in claim 8, characterized in that, The specific method for obtaining the perturbed predicted expression profile through the expression profile format conversion module is as follows: based on the bin representative value corresponding to the discretized predicted expression profile of the gene, the discretized predicted expression profile is dequantized into a continuous raw expression profile. Then, the continuous raw expression profile, perturbation conditions, and covariates are passed through a multilayer perceptron to output the perturbed predicted expression profile.

10. A single-cell perturbation response prediction system based on a modulated enhanced discrete diffusion model, characterized in that, This method is used to implement the single-cell perturbation response prediction method based on the regulated enhanced discrete diffusion model as described in any one of claims 1 to 9.

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