An image generation method and device based on a heat kernel theory on a riemannian manifold
By employing the image generation method based on the thermal kernel theory of Riemannian manifolds, and utilizing a geometric encoder and decoder to process image data on low-dimensional manifolds, this method solves the problems of high computational resource consumption and insufficient data quality in traditional methods, and achieves efficient and stable image generation.
Patent Information
- Application Number
- CN202411135883.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-08-19
- Publication Date
- 2025-11-28
- Estimated Expiration
- 2044-08-19
AI Technical Summary
Traditional image generation techniques suffer from high computational resource consumption, long processing time, and insufficient quality and diversity of generated data in high-dimensional data processing, especially in diffusion models where it is difficult to effectively capture the complexity of the data.
An image generation method based on the thermal kernel theory on Riemannian manifolds is adopted. By acquiring high-dimensional Euclidean space image data, unsupervised learning is performed using a geometric encoder and decoder to map it onto a low-dimensional Riemannian manifold. The inverse diffusion process is then carried out through the diffusion equation and the thermal kernel generation model on the Riemannian manifold to improve the learning accuracy and efficiency.
It reduces computational resources and time consumption, improves the quality and diversity of image generation, enhances the training stability and convergence of the model, and generates more realistic and diverse images.
Smart Images

Figure CN119130785B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The application belongs to the technical field of image generation, and particularly relates to an image generation method and device based on heat kernel theory on Riemannian manifold. BACKGROUND
[0002] Image generation refers to the use of computer algorithms and techniques to create new images through processing and learning of existing information. This technology can include generating completely new images from scratch, or modifying, enhancing, or synthesizing existing images. In image generation, computer systems can learn from a large amount of image data to extract rules and features, so as to generate images with realistic and artistic feeling. The development of this field has brought significant impact to many fields, including computer vision, medical image processing, artistic creation, etc.
[0003] The core of image generation technology lies in the learning and inference ability of the model, which is usually implemented using deep learning and neural network models. These models can understand the features and structures of images through large-scale data training, and can generate new images comparable to real images. This technology has a wide range of applications, including computer graphics, virtual reality, medical image processing, image enhancement, video game development, etc. With the continuous progress of technology, image generation technology will continue to bring more innovation and convenience to people's life and work.
[0004] Traditional diffusion model training process usually involves complex steps, which need to simulate the diffusion process step by step, requiring a large amount of computing resources and time; processing high-dimensional data may encounter convergence difficulty, and the quality of generated data may be affected by the complexity of the model; the diffusion model may lose the diversity of the original data during the generation process, resulting in a lack of diversity in the generated data. SUMMARY
[0005] In view of the problems existing in the prior art, the application provides an image generation method and device based on heat kernel theory on Riemannian manifold.
[0006] According to a first aspect of an embodiment of the application, an image generation method based on heat kernel theory on Riemannian manifold is provided, comprising:
[0007] Obtaining a target image data set in a high-dimensional Euclidean space, and preprocessing the target image data set;
[0008] Considering the Riemannian geometric structure of the target image data distribution, training a geometric encoder and a geometric decoder through an unsupervised learning method;
[0009] Mapping the target image data set through the trained geometric encoder to a low-dimensional Riemannian manifold to obtain a target data distribution on the low-dimensional manifold;
[0010] mapping the target data distribution as a normal distribution on the low-dimensional manifold by diffusion equation, and learning the inverse diffusion process of the normal distribution to the target data distribution by heat kernel on Riemannian manifold generation model;
[0011] sampling from the normal distribution on the low-dimensional manifold, estimating the data distribution on the high-dimensional manifold by heat kernel on Riemannian manifold generation model, and restoring the image distribution in the high-dimensional Euclidean space by the geometric decoder, thereby completing the image generation.
[0012] Further, the target image data set at least includes images of a required generation category.
[0013] Further, the geometric encoder is used to convert high-dimensional image data into low-dimensional manifold representation, and the geometric decoder is used to reconstruct the low-dimensional manifold representation into high-dimensional image data.
[0014] Further, the loss function used in the training of the geometric encoder and the geometric decoder includes reconstruction loss, LIPIS loss and local distortion measure of the mapping f between Riemannian manifolds, and the local distortion measure is:
[0015]
[0016] wherein d i is an element of the diagonal matrix D, λ i (z) represents an eigenvalue of the Riemannian metric G(z), and z is a local coordinate of the low-dimensional Riemannian manifold with dimension m.
[0017] Further, the diffusion equation is:
[0018]
[0019] wherein, is a point in the latent space, t∈[0,T], T refers to the end point of diffusion time, p t (x t ) refers to the probability distribution at t time, f t (x t ) is a drift coefficient, σ t is the variance of the normal distribution at t time.
[0020] Further, in the learning process of the heat kernel on Riemannian manifold generation model, the loss function is a heat kernel score matching loss, specifically:
[0021]
[0022] wherein, is a point in the latent space, t∈[0,T], T denotes the end of the diffusion time, f t (x t )=s θ (x t ,t) is the drift coefficient.
[0023] According to a second aspect of the embodiments of the present application, an image generation device based on a heat kernel theory on a Riemannian manifold is provided, comprising:
[0024] An acquisition module is configured to acquire a target image data set in a high-dimensional Euclidean space, and pre-process the target image data set.
[0025] A first training module is configured to consider a Riemannian geometric structure of a target image data distribution, and train a geometric encoder and a geometric decoder by using an unsupervised learning method.
[0026] A mapping module is configured to map the target image data set to a low-dimensional Riemannian manifold by using the trained geometric encoder, to obtain a target data distribution on the low-dimensional manifold.
[0027] A second training module is configured to map the target data distribution to a normal distribution on the low-dimensional manifold by using a diffusion equation, and learn an inverse diffusion process from the normal distribution to the target data distribution by using a heat kernel generation model on the Riemannian manifold.
[0028] An image generation module is configured to sample from the normal distribution on the low-dimensional manifold, estimate a data distribution on a high-dimensional manifold by using the heat kernel generation model on the Riemannian manifold, and restore the image distribution to the high-dimensional Euclidean space by using the geometric decoder, so as to complete the image generation.
[0029] According to a third aspect of the embodiments of the present application, a computer program product is provided, comprising computer programs / instructions, which, when executed by a processor, implement the method according to the first aspect.
[0030] According to a fourth aspect of the embodiments of the present application, an electronic device is provided, comprising:
[0031] one or more processors;
[0032] a memory configured to store one or more programs;
[0033] When the one or more programs are executed by the one or more processors, the one or more processors implement the method according to the first aspect.
[0034] According to a fifth aspect of the embodiments of the present application, a computer readable storage medium is provided, which stores computer instructions, and the instructions, when executed by a processor, implement the steps of the method according to the first aspect.
[0035] The technical scheme provided by the embodiment of the present application can include the following beneficial effects:
[0036] As can be seen from the above embodiments, the present application limits the Riemannian metric training geometric encoder and geometric decoder, learns the representation of the image in the low-dimensional manifold, maps the target data distribution to a special distribution on the low-dimensional manifold through the diffusion equation, and learns the inverse diffusion process with a neural network to improve the learning accuracy and learning efficiency. When performing an image generation task, sample from the special distribution on the low-dimensional manifold, estimate the target data distribution on the low-dimensional manifold through the heat kernel generation model on the Riemannian manifold, and restore to the image distribution in the high-dimensional Euclidean space through the geometric decoder. The diffusion equation can provide a more effective training method, reducing the consumption of computing resources and time; the characteristics of Riemannian geometry can help the heat kernel generation model on the Riemannian manifold to converge better in high-dimensional space, improving the stability and effect of training; using the structure of Riemannian geometry, the heat kernel generation model on the Riemannian manifold can more accurately capture the complexity of the data, thereby generating higher quality and more diverse images.
[0037] It should be understood that the foregoing general description and the following detailed description are only exemplary and explanatory, and cannot limit the present application. BRIEF DESCRIPTION OF DRAWINGS
[0038] The accompanying drawings, which are incorporated into and form part of the specification, illustrate an embodiment consistent with the present application and, together with the description, serve to explain the principles of the application.
[0039] Figure 1 FIG. 1 is a flowchart of an image generation method based on heat kernel theory on a Riemannian manifold according to an exemplary embodiment.
[0040] Figure 2 FIG. 2 is a block diagram of an image generation device based on heat kernel theory on a Riemannian manifold according to an exemplary embodiment.
[0041] Figure 3 FIG. 3 is a schematic diagram of an electronic device according to an exemplary embodiment. DETAILED DESCRIPTION
[0042] The exemplary embodiments will be described in detail herein with reference to the accompanying drawings. In the following description, the same numbers refer to the same elements throughout the drawings, unless otherwise represented. The embodiments described in the following exemplary embodiments do not represent all the embodiments consistent with the present application.
[0043] The terminology used in this application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application. As used in this application and the appended claims, the singular forms "a," "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will also be understood that the term "and / or," as used herein, refers to and encompasses any and all possible combinations of one or more of the associated listed items.
[0044] It is to be understood that the terms first, second, third, etc. that are used in this specification are not intended to denote any utmost specific sequence of information but are used to distinguish between different types of information. For example, the first information can also be referred to as the second information and similarly the second information can also be referred to as the first information without departing from the scope of the application. Depending on the context, the word "if' as used herein can be interpreted to mean "when" or "in response to determining".
[0045] The application provides an image generation method based on heat kernel theory on Riemannian manifold, limits Riemannian metric learning geometric encoder and geometric decoder, learns the representation of image in low-dimensional manifold, and carries out heat diffusion and learning inverse diffusion process on Riemannian manifold, improves the learning accuracy and learning efficiency. The sampling process is to sample from a special distribution on a low-dimensional manifold, estimate the target data distribution on the low-dimensional manifold through the heat kernel generation model on the Riemannian manifold, and restore the image distribution in the high-dimensional Euclidean space through the geometric decoder.
[0046] Please refer to Figure 1 As shown in the figure, comprising the following steps:
[0047] (1) obtaining a target image data set in a high-dimensional Euclidean space, and preprocessing the target image data set;
[0048] Specifically, the application selects MNIST data set, CIFAR-10 data set, MNIST data set is a commonly used handwritten digital data set, which is composed of digital images from 0 to 9. Each image is a gray image with a size of 28x28 pixels. This data set contains 60000 training images and 10000 test images, and the training images and test images are combined; the CIFAR-10 data set includes 10 different categories of color images, each category has 6000 images. These categories include airplane, car, bird, cat, deer, dog, frog, horse, ship and truck. The size of each image is 32x32 pixels. The above images are combined as a target image data set, and the preprocessing operation on it can include one or more of image center cropping, image random cropping and image enhancement.
[0049] It should be noted that the target image data set at least includes images of the required generated category, and in addition to the images of the required generated category, images of other categories can also be included.
[0050] (2) Considering the Riemannian geometric structure of the target image data distribution, training the geometric encoder and the geometric decoder by an unsupervised learning method;
[0051] First, the autoencoder that preserves the geometric mapping between two Riemannian manifolds. Let be a Riemannian manifold of dimension m, with local coordinates Riemannian metric G(z) e R m×m , be a Riemannian manifold of dimension n, with local coordinates Riemannian metric H(x) e R n×n Let the geometric decoder be a smooth mapping, expressed in local coordinates as f: The differential of the mapping f is expressed by the Jacobian matrix
[0052] Intuitively, keeping independent mapping means that the metric values in different coordinate axis directions are independent of each other. In local coordinates, the mapping f: between Riemannian manifolds is an independent mapping if and only if:
[0053]
[0054] Throughout the process, it is assumed that the latent space and the data space are Riemannian manifolds, where the latent space is endowed with a diagonal metric, and the environment data space is endowed with a Riemannian metric H(x), and the pullback metric is defined as G(z).
[0055] In order to do the heat kernel generative model in the low-dimensional manifold, it is necessary to make the pullback metric G(z) = D, D is a diagonal matrix, then f: is an independent mapping if and only if:
[0056]
[0057] If all eigenvalues of J f (z) T H(f(z))J f (z) are equal to 1, then the mapping f is an isometric mapping, and D is a diagonal matrix. Here, {λ i (z)} represents the eigenvalues of the Riemannian metric G(z), and the local distortion metric of f can be defined, which measures how far the mapping f is from local isometry, as follows:
[0058]
[0059] This local measure can be integrated with some probability measure v (in units) to define a global distortion measure:
[0060]
[0061] Since the influence of the measure is limited to the support of v, if the global distortion measure of f is zero, then f is a preserving independent map with respect to the support of v. The local distortion measure is considered as a local distortion measure, but this measure is not coordinate-invariant. The local distortion measure defined by the eigenvalues is coordinate-invariant, so it is well-defined geometrically. This is the general strategy for constructing coordinate-invariant functionals on Riemannian manifolds and the general formula for coordinate-invariant distortion measures.
[0062] In addition to the reconstruction loss and LIPIS loss are added to maintain the realism of the image.
[0063] Geometric autoencoder is a model for learning low-dimensional representation of data. It adds restrictions on the metric of the latent space in the traditional autoencoder architecture, so that the encoded representation has more geometric meaning. The input of the geometric encoder is a sample point in the high-dimensional space For image data X, the input is a tensor of (H, W, C), where n = H x W x C, and H and W are the height and width of the image, and C is the number of channels. The output of the geometric encoder is a representation z on a low-dimensional manifold , which is a vector of dimension m, which encodes the input data into a low-dimensional representation through several layers of neural networks such as convolutional layers and fully connected layers. Correspondingly, the input of the geometric decoder is a representation z on a low-dimensional manifold, which is decoded into high-dimensional data output through several layers of neural networks such as fully connected layers and convolutional layers, which is the reconstructed high-dimensional image data sample. The shape of the reconstructed image data is (H, W, C), which should be consistent with the shape of the input. The geometric autoencoder adds constraints on the geometric structure of the latent space based on the traditional autoencoder. The constraint used here is the local distortion measure.
[0064] (3) mapping the target image data set through the trained geometric encoder to a low-dimensional Riemannian manifold to obtain a target data distribution on the low-dimensional manifold;
[0065] The target image data set is mapped to a low-dimensional Riemannian manifold, thereby obtaining the distribution of the target data on the low-dimensional manifold. The purpose of this method is to represent high-dimensional image data as a low-dimensional manifold structure through the geometric encoder, so that the representation of the data is more compact and easier to process. Such processing helps to model and analyze data in a lower dimension, and can help to discover the underlying structure and patterns in the data.
[0066] Assuming the distribution of the image is p(x), the geometric autoencoder maps the data distribution to p(z).
[0067] (4) Map the target data distribution to a normal distribution on a low-dimensional manifold by a diffusion equation, and learn the inverse diffusion process of the normal distribution to the target data distribution by a heat kernel generation model on the Riemannian manifold;
[0068] The geometric autoencoder designs the hidden space, and uses the pullback metric to define the Riemannian metric of the Riemannian manifold on the original space, and designs the heat kernel generation algorithm of the general manifold. According to the foregoing, it is necessary to learn a Riemannian metric G(z) on the hidden space, that is, the pullback metric, and on this basis, design the heat kernel generation algorithm. Set H(x) = D = I, where I is the unit matrix, then the Riemannian metric of the hidden space can be directly defined, that is:
[0069]
[0070] Stable Diffusion regards the space learned by the autoencoder as a Euclidean space, which is unreasonable because its Riemannian metric is not a unit matrix. Therefore, the present application first designs a geometric autoencoder to project the original space into a Euclidean space, and designs a heat kernel generation algorithm on the space.
[0071] First, we consider a point in the hidden space t∈[0,T] of a constant differential equation:
[0072]
[0073] Where T refers to the end point of the diffusion time, generally taken as 1, f t (x t ) is the drift coefficient;
[0074] It describes a continuous and reversible transformation from x0 to x T If x0 is a random variable, then x t in the whole process is also a random variable, and its distribution change rule can be described by the following equation derived from the Fokker-Planck equation:
[0075]
[0076] Where p t (x t ) refers to the probability distribution at time t, and it is assumed that
[0077]
[0078] A heat equation for the probability density can be obtained:
[0079]
[0080] where the initial value is p(x, 0) = p0, p0 represents a normal distribution, p(x, 0) is the distribution of x at time 0. By using Fourier transform, the heat conduction equation can be converted into an ordinary differential equation, so as to obtain the solution distribution p t (x t ). Fourier transform can be performed on both ends of the above equation to transform it into the frequency domain, so there is:
[0081]
[0082] where i is the imaginary unit, and w is the frequency;
[0083] Then a constant differential equation can be obtained:
[0084]
[0085] An analytical solution can be obtained through the ordinary differential equation:
[0086]
[0087] where σ t is the variance of the normal distribution at time t. Through inverse Fourier transform, the solution distribution p t (x t ) can be obtained:
[0088]
[0089] Then the probability transition density, i.e., the analytical solution of the heat kernel, can be obtained:
[0090]
[0091] The heat kernel score matching loss can be obtained, and a neural network is used to fit the drift coefficient f t (x t ) = s θ (x t , t):
[0092]
[0093] The heat kernel generation model is completed on the latent space.
[0094] It should be noted that the neural network is not limited here, and it only needs to meet the dimension requirements of the input and output.
[0095] The heat kernel generation model takes the heat kernel score matching loss as a loss function, is trained by an Adam optimizer, and when the optimized model reaches or exceeds an evaluation index, a trained heat kernel generation model on a Riemannian manifold is obtained.
[0096] (5) Sampling from a normal distribution on a low-dimensional manifold (Euclidean space), estimating the data distribution on a high-dimensional manifold by a heat kernel generation model on a Riemannian manifold, and restoring the image distribution in a high-dimensional Euclidean space by a geometric decoder, thereby completing image generation.
[0097] Corresponding to the foregoing embodiments of the image generation method based on the heat kernel theory on a Riemannian manifold, the present application also provides embodiments of an image generation device based on the heat kernel theory on a Riemannian manifold.
[0098] Figure 2 is a block diagram of an image generation device based on the heat kernel theory on a Riemannian manifold according to an exemplary embodiment.
[0099] Referring to Figure 2 , the device can include:
[0100] An acquisition module 21 is configured to acquire a target image data set in a high-dimensional Euclidean space, and pre-process the target image data set.
[0101] A first training module 22 is configured to train a geometric encoder and a geometric decoder by an unsupervised learning method, taking into account the Riemannian geometric structure of the target image data distribution.
[0102] A mapping module 23 is configured to map the target image data set through the trained geometric encoder to a low-dimensional Riemannian manifold, to obtain a target data distribution on the low-dimensional manifold.
[0103] A second training module 24 is configured to map the target data distribution to a normal distribution on the low-dimensional manifold by a diffusion equation, and learn an inverse diffusion process from the normal distribution to the target data distribution by a heat kernel generation model on a Riemannian manifold.
[0104] An image generation module 25 is configured to sample from the normal distribution on the low-dimensional manifold, estimate the data distribution on the high-dimensional manifold by the heat kernel generation model on the Riemannian manifold, and restore the image distribution in the high-dimensional Euclidean space by the geometric decoder, thereby completing image generation.
[0105] As to the device in the foregoing embodiments, the specific manner in which each module performs operations has been described in detail in the embodiments of the method, and will not be described in detail here.
[0106] For the apparatus embodiment, since it basically corresponds to the method embodiment, the relevant part can be seen from the part of the method embodiment. The apparatus embodiment described above is only illustrative, wherein the units described as separate components can or can not be physically separated, and the components displayed as units can or can not be physical units, i.e., can be located in one place or distributed on multiple network units. Part or all of the modules can be selected to achieve the purpose of the application according to actual needs. Those skilled in the art can understand and implement without creative labor.
[0107] Correspondingly, the application also provides a computer program product, comprising computer programs / instructions, which, when executed by a processor, implement the image generation method based on the heat kernel theory on Riemannian manifold as described above.
[0108] Correspondingly, the application also provides an electronic device, comprising: one or more processors; a memory for storing one or more programs; when the one or more programs are executed by the one or more processors, the one or more processors implement the image generation method based on the heat kernel theory on Riemannian manifold as described above. As Figure 3 As shown in the figure, a hardware structure diagram of an apparatus for generating images based on the heat kernel theory on Riemannian manifold provided by the embodiment of the application is in any data processing capable device. In addition to the processor, the memory and the network interface shown in the figure, the apparatus in the embodiment is usually provided in any data processing capable device according to the actual function of the data processing capable device, which can also include other hardware, and this will not be described again. Figure 3 As shown in the figure, a hardware structure diagram of an apparatus for generating images based on the heat kernel theory on Riemannian manifold provided by the embodiment of the application is in any data processing capable device. In addition to the processor, the memory and the network interface shown in the figure, the apparatus in the embodiment is usually provided in any data processing capable device according to the actual function of the data processing capable device, which can also include other hardware, and this will not be described again.
[0109] Correspondingly, the application also provides a computer readable storage medium, which stores computer instructions, and the instructions, when executed by a processor, implement the image generation method based on the heat kernel theory on Riemannian manifold as described above. The computer readable storage medium can be an internal storage unit of any data processing capable device, such as a hard disk or a memory. The computer readable storage medium can also be an external storage device, such as a plug-in hard disk, a smart media card (SMC), an SD card, a flash card, etc. Further, the computer readable storage medium can include both the internal storage unit of any data processing capable device and the external storage device. The computer readable storage medium is used to store the computer program and other programs and data required by the data processing capable device, and can also be used to temporarily store data that has been output or will be output.
[0110] Other embodiments of the application will be apparent to those skilled in the art from consideration of the specification and practice of the application disclosed herein. It is intended that the application embrace any and all variations, modifications, and adaptations of the application described herein, which are within the scope of the general inventive concept and include those expressly described herein, as well as other combinations of features, functions, and concepts included in the present disclosure or that are inherent in this field of technology.
[0111] It is to be understood that the application is not limited to the precise construction here described and as shown in the drawings, and that various modifications and changes can be made by those skilled in the art without departing from the scope of the application.
Claims
1. An image generation method based on the Riemannian manifold thermal kernel theory, characterized in that, include: Obtain the target image dataset in high-dimensional Euclidean space and preprocess the target image dataset; Considering the Riemannian geometric structure of the target image data distribution, a geometric encoder and a geometric decoder are trained using an unsupervised learning method; The target image dataset is mapped onto a low-dimensional Riemannian manifold through a trained geometric encoder to obtain the target data distribution on the low-dimensional manifold. The target data distribution is mapped to a normal distribution on a low-dimensional manifold using a diffusion equation, and the inverse diffusion process from the normal distribution to the target data distribution is learned using a thermal kernel generation model on a Riemannian manifold. Image generation is achieved by sampling from the normal distribution on a low-dimensional manifold, estimating the data distribution on a high-dimensional manifold using a hot kernel generation model on a Riemannian manifold, and then restoring the image distribution to the high-dimensional Euclidean space using a geometric decoder.
2. The method according to claim 1, characterized in that, The target image dataset includes at least the images of the desired generation category.
3. The method according to claim 1, characterized in that, The geometric encoder is used to convert high-dimensional image data into a low-dimensional manifold representation, and the geometric decoder is used to reconstruct the low-dimensional manifold representation into high-dimensional image data.
4. The method according to claim 1, characterized in that, The loss functions used during the training of the geometric encoder and geometric decoder include reconstruction loss, LiPIS loss, and mapping between Riemannian manifolds. The local distortion measure is: , in, These are the elements of the diagonal matrix D. Representing Riemannian metric eigenvalues, For dimension is Local coordinates of a low-dimensional Riemannian manifold.
5. The method according to claim 1, characterized in that, The diffusion equation is: , in, Let be a point in the latent space. , , This refers to the end of the diffusion time. This refers to the probability distribution at time t. The drift coefficient, , Let be the variance of the normal distribution at time t.
6. The method according to claim 1, characterized in that, In the learning process of the hot kernel generation model on the Riemannian manifold, the loss function is the hot kernel score matching loss, specifically: , in, Let be a point in the latent space. , , This refers to the end of the diffusion time. The drift coefficient, It is a random variable. Let be the variance of the normal distribution at time t, and I be the identity matrix.
7. An image generation method based on the Riemannian manifold thermal kernel theory, characterized in that, include: The acquisition module is used to acquire the target image dataset in high-dimensional Euclidean space and preprocess the target image dataset. The first training module is used to consider the Riemannian geometric structure of the target image data distribution and train the geometric encoder and geometric decoder through unsupervised learning methods. The mapping module is used to map the target image dataset onto a low-dimensional Riemannian manifold through a trained geometric encoder to obtain the target data distribution on the low-dimensional manifold. The second training module is used to map the target data distribution to a normal distribution on a low-dimensional manifold through a diffusion equation, and to learn the inverse diffusion process from the normal distribution to the target data distribution using a thermal kernel generation model on a Riemannian manifold. The image generation module samples from a normal distribution on a low-dimensional manifold, estimates the data distribution on a high-dimensional manifold using a hot kernel generation model on a Riemannian manifold, and restores the image distribution to high-dimensional Euclidean space using a geometric decoder, thereby completing image generation.
8. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instruction is executed by the processor, it implements the method as described in any one of claims 1-6.
9. An electronic device, characterized in that, include: One or more processors; Memory, used to store one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the method as described in any one of claims 1-6.
10. A computer-readable storage medium storing computer instructions thereon, characterized in that, When executed by the processor, this instruction implements the steps of the method as described in any one of claims 1-6.
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