Flow Map Learning via Nongradient Vector Flow

• URL: http://arxiv.org/abs/2607.26398v1
• Date: Wed, 29 Jul 2026 02:17:27 GMT
• Title: Flow Map Learning via Nongradient Vector Flow
• Abstract summary: Diffusion and flow-based models benefit from simple regression losses, but inference incurs significant overhead because sampling requires integration.<n>We introduce SGFlow, an approach for learning flow maps that bypasses explicit invertibility constraints and expensive differentiation through model iteration.
• Score: 22.985676782036904
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

Related papers

• Flow-Map GRPO: Reinforcement Learning for Few-Step Flow-Map Generators via Anchored Stochastic Composition [13.766141027420879]
  Few-step flow-map generators, such as consistency models and MeanFlow, accelerate sampling by directly learning longrange transport maps between noise and data.<n>These models are typically deterministic, which makes them difficult to optimize with post-training methods.<n>We propose Flow-MapO, an online framework for deterministic post-training framework for fewstep flow-map generators.
  arXiv  Detail & Related papers  (2026-07-01T07:25:11Z)
• AnyFlow: Any-Step Video Diffusion Model with On-Policy Flow Map Distillation [70.80207977907908]
  We introduce AnyFlow, the first any-step video diffusion distillation framework based on flow maps.<n>We show that AnyFlow achieves performance matches or surpasses consistency-based counterparts in the few-step regime.
  arXiv  Detail & Related papers  (2026-05-13T16:06:34Z)
• Trajectory Stitching for Solving Inverse Problems with Flow-Based Models [68.36374645801901]
  Flow-based generative models have emerged as powerful priors for solving inverse problems.<n>We propose MS-Flow, which represents the trajectory as a sequence of intermediate latent states rather than a single initial code.<n>We demonstrate the effectiveness of MS-Flow over existing methods on image recovery and inverse problems, including inpainting, super-resolution, and computed tomography.
  arXiv  Detail & Related papers  (2026-02-09T11:36:41Z)
• FlowConsist: Make Your Flow Consistent with Real Trajectory [99.22869983378062]
  We argue that current fast-flow training paradigms suffer from two fundamental issues.<n> conditional velocities constructed from randomly paired noise-data samples introduce systematic trajectory drift.<n>We propose FlowConsist, a training framework designed to enforce trajectory consistency in fast flows.
  arXiv  Detail & Related papers  (2026-02-06T03:24:23Z)
• SoFlow: Solution Flow Models for One-Step Generative Modeling [10.054000663262618]
  Flow Models (SoFlow) is a framework for one-step generation from scratch.<n>Flow Matching loss allows our models to provide estimated velocity fields during training.<n>Our models achieve better FID-50K scores than MeanFlow models on the ImageNet 256x256 dataset.
  arXiv  Detail & Related papers  (2025-12-17T18:10:17Z)
• Decoupled MeanFlow: Turning Flow Models into Flow Maps for Accelerated Sampling [68.76215229126886]
  We introduce Decoupled MeanFlow, a simple decoding strategy that converts flow models into flow map models without architectural modifications.<n>Our method conditions the final blocks of diffusion transformers on the subsequent timestep, allowing pretrained flow models to be directly repurposed as flow maps.<n>On ImageNet 256x256 and 512x512, our models attain 1-step FID of 2.16 and 2.12, respectively, surpassing prior art by a large margin.
  arXiv  Detail & Related papers  (2025-10-28T14:43:48Z)
• Align Your Flow: Scaling Continuous-Time Flow Map Distillation [63.927438959502226]
  Flow maps connect any two noise levels in a single step and remain effective across all step counts.<n>We extensively validate our flow map models, called Align Your Flow, on challenging image generation benchmarks.<n>We show text-to-image flow map models that outperform all existing non-adversarially trained few-step samplers in text-conditioned synthesis.
  arXiv  Detail & Related papers  (2025-06-17T15:06:07Z)
• How to build a consistency model: Learning flow maps via self-distillation [18.299322342860517]
  Flow-based generative models achieve state-of-the-art sample quality, but require the expensive solution of a differential equation at inference time.<n>These models lack a unified description that clearly explains how to learn them efficiently in practice.<n>We present a systematic algorithmic framework for directly learning the flow map associated with a flow or diffusion model.
  arXiv  Detail & Related papers  (2025-05-24T18:50:50Z)
• Rectified Diffusion: Straightness Is Not Your Need in Rectified Flow [65.51671121528858]
  Diffusion models have greatly improved visual generation but are hindered by slow generation speed due to the computationally intensive nature of solving generative ODEs. Rectified flow, a widely recognized solution, improves generation speed by straightening the ODE path. We propose Rectified Diffusion, which generalizes the design space and application scope of rectification to encompass the broader category of diffusion models.
  arXiv  Detail & Related papers  (2024-10-09T17:43:38Z)
• Optimal Flow Matching: Learning Straight Trajectories in Just One Step [89.37027530300617]
  We develop and theoretically justify the novel textbf Optimal Flow Matching (OFM) approach. It allows recovering the straight OT displacement for the quadratic transport in just one FM step. The main idea of our approach is the employment of vector field for FM which are parameterized by convex functions.
  arXiv  Detail & Related papers  (2024-03-19T19:44:54Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.