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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.09665 |
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| _version_ | 1866907974734184448 |
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| author | Zhang, Xicheng |
| author_facet | Zhang, Xicheng |
| contents | Drawing from the theory of stochastic differential equations, we introduce a novel sampling method for known distributions and a new algorithm for diffusion generative models with unknown distributions. Our approach is inspired by the concept of the reverse diffusion process, widely adopted in diffusion generative models. Additionally, we derive the explicit convergence rate based on the smooth ODE flow. For diffusion generative models and sampling, we establish a dimension-free particle approximation convergence result. Numerical experiments demonstrate the effectiveness of our method. Notably, unlike the traditional Langevin method, our sampling method does not require any regularity assumptions about the density function of the target distribution. Furthermore, we also apply our method to optimization problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_09665 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | New algorithms for sampling and diffusion models Zhang, Xicheng Statistics Theory Optimization and Control Probability Machine Learning 60H10 Drawing from the theory of stochastic differential equations, we introduce a novel sampling method for known distributions and a new algorithm for diffusion generative models with unknown distributions. Our approach is inspired by the concept of the reverse diffusion process, widely adopted in diffusion generative models. Additionally, we derive the explicit convergence rate based on the smooth ODE flow. For diffusion generative models and sampling, we establish a dimension-free particle approximation convergence result. Numerical experiments demonstrate the effectiveness of our method. Notably, unlike the traditional Langevin method, our sampling method does not require any regularity assumptions about the density function of the target distribution. Furthermore, we also apply our method to optimization problems. |
| title | New algorithms for sampling and diffusion models |
| topic | Statistics Theory Optimization and Control Probability Machine Learning 60H10 |
| url | https://arxiv.org/abs/2406.09665 |