An Eulerian Perspective on Straight-Line Sampling
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909955856007168 |
|---|---|
| author | Tsimpos, Panos Marzouk, Youssef |
| author_facet | Tsimpos, Panos Marzouk, Youssef |
| contents | We study dynamic measure transport for generative modeling: specifically, flows induced by stochastic processes that bridge a specified source and target distribution. The conditional expectation of the process' velocity defines an ODE whose flow map achieves the desired transport. We ask \emph{which processes produce straight-line flows} -- i.e., flows whose pointwise acceleration vanishes and thus are exactly integrable with a first-order method? We provide a concise PDE characterization of straightness as a balance between conditional acceleration and the divergence of a weighted covariance (Reynolds) tensor. Using this lens, we fully characterize affine-in-time interpolants and show that straightness occurs exactly under deterministic endpoint couplings. We also derive necessary conditions that constrain flow geometry for general processes, offering broad guidance for designing transports that are easier to integrate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_11657 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Eulerian Perspective on Straight-Line Sampling Tsimpos, Panos Marzouk, Youssef Machine Learning We study dynamic measure transport for generative modeling: specifically, flows induced by stochastic processes that bridge a specified source and target distribution. The conditional expectation of the process' velocity defines an ODE whose flow map achieves the desired transport. We ask \emph{which processes produce straight-line flows} -- i.e., flows whose pointwise acceleration vanishes and thus are exactly integrable with a first-order method? We provide a concise PDE characterization of straightness as a balance between conditional acceleration and the divergence of a weighted covariance (Reynolds) tensor. Using this lens, we fully characterize affine-in-time interpolants and show that straightness occurs exactly under deterministic endpoint couplings. We also derive necessary conditions that constrain flow geometry for general processes, offering broad guidance for designing transports that are easier to integrate. |
| title | An Eulerian Perspective on Straight-Line Sampling |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2510.11657 |