Diffusion at Absolute Zero: Langevin Sampling Using Successive Moreau Envelopes [conference paper]
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915224335941632 |
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| author | Habring, Andreas Falk, Alexander Pock, Thomas |
| author_facet | Habring, Andreas Falk, Alexander Pock, Thomas |
| contents | In this article we propose a novel method for sampling from Gibbs distributions of the form $π(x)\propto\exp(-U(x))$ with a potential $U(x)$. In particular, inspired by diffusion models we propose to consider a sequence $(π^{t_k})_k$ of approximations of the target density, for which $π^{t_k}\approx π$ for $k$ small and, on the other hand, $π^{t_k}$ exhibits favorable properties for sampling for $k$ large. This sequence is obtained by replacing parts of the potential $U$ by its Moreau envelopes. Sampling is performed in an Annealed Langevin type procedure, that is, sequentially sampling from $π^{t_k}$ for decreasing $k$, effectively guiding the samples from a simple starting density to the more complex target. In addition to a theoretical analysis we show experimental results supporting the efficacy of the method in terms of increased convergence speed and applicability to multi-modal densities $π$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_01358 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Diffusion at Absolute Zero: Langevin Sampling Using Successive Moreau Envelopes [conference paper] Habring, Andreas Falk, Alexander Pock, Thomas Optimization and Control Computer Vision and Pattern Recognition Numerical Analysis 65C40, 65C05, 68U10, 65C60 G.3; G.1.6 In this article we propose a novel method for sampling from Gibbs distributions of the form $π(x)\propto\exp(-U(x))$ with a potential $U(x)$. In particular, inspired by diffusion models we propose to consider a sequence $(π^{t_k})_k$ of approximations of the target density, for which $π^{t_k}\approx π$ for $k$ small and, on the other hand, $π^{t_k}$ exhibits favorable properties for sampling for $k$ large. This sequence is obtained by replacing parts of the potential $U$ by its Moreau envelopes. Sampling is performed in an Annealed Langevin type procedure, that is, sequentially sampling from $π^{t_k}$ for decreasing $k$, effectively guiding the samples from a simple starting density to the more complex target. In addition to a theoretical analysis we show experimental results supporting the efficacy of the method in terms of increased convergence speed and applicability to multi-modal densities $π$. |
| title | Diffusion at Absolute Zero: Langevin Sampling Using Successive Moreau Envelopes [conference paper] |
| topic | Optimization and Control Computer Vision and Pattern Recognition Numerical Analysis 65C40, 65C05, 68U10, 65C60 G.3; G.1.6 |
| url | https://arxiv.org/abs/2502.01358 |