Theoretical guarantees in KL for Diffusion Flow Matching
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916391696728064 |
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| author | Silveri, Marta Gentiloni Conforti, Giovanni Durmus, Alain |
| author_facet | Silveri, Marta Gentiloni Conforti, Giovanni Durmus, Alain |
| contents | Flow Matching (FM) (also referred to as stochastic interpolants or rectified flows) stands out as a class of generative models that aims to bridge in finite time the target distribution $ν^\star$ with an auxiliary distribution $μ$, leveraging a fixed coupling $π$ and a bridge which can either be deterministic or stochastic. These two ingredients define a path measure which can then be approximated by learning the drift of its Markovian projection. The main contribution of this paper is to provide relatively mild assumptions on $ν^\star$, $μ$ and $π$ to obtain non-asymptotics guarantees for Diffusion Flow Matching (DFM) models using as bridge the conditional distribution associated with the Brownian motion. More precisely, we establish bounds on the Kullback-Leibler divergence between the target distribution and the one generated by such DFM models under moment conditions on the score of $ν^\star$, $μ$ and $π$, and a standard $L^2$-drift-approximation error assumption. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08311 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Theoretical guarantees in KL for Diffusion Flow Matching Silveri, Marta Gentiloni Conforti, Giovanni Durmus, Alain Machine Learning Probability Flow Matching (FM) (also referred to as stochastic interpolants or rectified flows) stands out as a class of generative models that aims to bridge in finite time the target distribution $ν^\star$ with an auxiliary distribution $μ$, leveraging a fixed coupling $π$ and a bridge which can either be deterministic or stochastic. These two ingredients define a path measure which can then be approximated by learning the drift of its Markovian projection. The main contribution of this paper is to provide relatively mild assumptions on $ν^\star$, $μ$ and $π$ to obtain non-asymptotics guarantees for Diffusion Flow Matching (DFM) models using as bridge the conditional distribution associated with the Brownian motion. More precisely, we establish bounds on the Kullback-Leibler divergence between the target distribution and the one generated by such DFM models under moment conditions on the score of $ν^\star$, $μ$ and $π$, and a standard $L^2$-drift-approximation error assumption. |
| title | Theoretical guarantees in KL for Diffusion Flow Matching |
| topic | Machine Learning Probability |
| url | https://arxiv.org/abs/2409.08311 |