Flow Map Learning via Nongradient Vector Flow
Mirrored from arXiv — Machine Learning for archival readability. Support the source by reading on the original site.
Computer Science > Machine Learning
Title:Flow Map Learning via Nongradient Vector Flow
Abstract:Diffusion and flow-based models benefit from simple regression losses, but inference incurs significant overhead because sampling requires integration. Consistency models address this by directly learning the flow maps along the ODE trajectory, opening a design space between one-step and many-step approaches. However, existing methods face computational challenges such as requiring model inverses or backpropagation through iterated model calls, and do not always prove that the desired ODE flow map is a solution to the loss. We introduce SGFlow, an approach for learning flow maps that bypasses explicit invertibility constraints and expensive differentiation through model iteration. SGFlow trains a model to compute both the ODE solutions and the implied velocity from scratch by following non-conservative dynamics with a stationary point at the desired flow map. On the CIFAR image benchmark, no single method attains the best FID at every step count: SGFlow attains the best FID at 10 sampling steps and remains competitive with flow matching, Meanflow, and Lagrangian map matching at other step counts, while being the only one with a proven stationary-point guarantee for its stopgrad-based dynamics.
| Comments: | ICLR 2026 |
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2607.26398 [cs.LG] |
| (or arXiv:2607.26398v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2607.26398
arXiv-issued DOI via DataCite (pending registration)
|
Access Paper:
- View PDF
- HTML (experimental)
- TeX Source
References & Citations
Bibliographic and Citation Tools
Code, Data and Media Associated with this Article
Demos
Recommenders and Search Tools
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
More from arXiv — Machine Learning
-
Learning Discrete Riemannian Metrics for Physical Fields with Cochain-Frame Equivarianc
Aug 18
-
Forward Pass Domain Adaptation (Without Cross-Layer Backpropagation)
Aug 18
-
Coarse-to-Fine Multi-Resolution Diffusion Models for Trajectory Generation in Urban Systems
Aug 18
-
Geometry Is Not Robustness: A Trajectory-Level Study of PGD Evaluation
Aug 18
Discussion (0)
Sign in to join the discussion. Free account, 30 seconds — email code or GitHub.
Sign in →No comments yet. Sign in and be the first to say something.