Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Language: English
Subfield: Computer Vision and Pattern Recognition
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: Deep probabilistic predictive models for stroke and coronary heart disease, G3329785188, G4353487559, NRT-HDR: FUTURE Foundations, Translation, and Responsibility for Data Science Impact, SCH: Multimodal representation learning and anomaly quantification for data-driven stroke rehabilitation, G6671297155, Career: Building Models that Avoid Spurious Correlations through Interpretability and Representation Learning, G8876996369
OpenAlex ID: W7171801325