mlsanityData to 14 Oct 2026

Strong Stochastic Flow Maps

arXiv 2606.01086 ↗First posted 31 May 2026cs.LG cs.AIcited by 6

On the map: Diffusion models → Diffusion foundations and sampling

Abstract (arXiv)

Flow and diffusion models generate high-quality samples in many modalities; however, many network evaluations are required during inference due to numerical integration of an underlying differential equation. Flow maps alleviate this problem by learning the solution map of the differential equation directly, enabling few-step sampling. Yet, current methods are restricted to approximating the solution map of ODEs. These methods can be used to learn the transition kernel of an SDE, thereby obtaining a solution map that recovers the marginal distributions of the process (weak convergence) rather than the solution path (strong convergence). We propose Strong Stochastic Flow Maps (SSFMs) as a novel framework for learning the strong solution map of additive-noise SDEs, directly generalizing deterministic flow maps to the stochastic setting. Further, a polynomial approximation to Brownian motion is introduced and shown to converge pathwise. These results enable a simulation-free training objective for the solution map of diffusion models. We demonstrate that SSFMs outperform previous stochastic flow map methods on image generation and enable few-step sampling of molecular systems.

Key facts. Cited by 6 papers in the map (data through 14 Oct 2026). Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models. Builds on 43 of its 60 references that are in the map. First posted on arXiv 31 May 2026.

Builds on

43 of 60 references.

Closest ancestors · 13

Same direction, newest first

  1. 2025Sig-DEG for Distillation: Making Diffusion Models Faster and Lighter23 Aug
  2. 2024One Step Diffusion via Shortcut Models16 Oct
  3. 2024Multistep Consistency Models11 Mar
  4. 2023Analyzing and Improving the Training Dynamics of Diffusion Models5 Dec
  5. 2023Improved Techniques for Training Consistency Models22 Oct
  6. 2023Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion1 Oct
  7. 2023SEEDS: Exponential SDE Solvers for Fast High-Quality Sampling from Diffusion Models23 May
  8. 2023Consistency Models2 Mar
  9. 2022DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps2 Jun
  10. 2022Fast Sampling of Diffusion Models with Exponential Integrator29 Apr
  11. 2021High-Resolution Image Synthesis with Latent Diffusion Models20 Dec
  12. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov
1 more
  1. 2020Denoising Diffusion Probabilistic Models19 Jun

Other references · 30

  1. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,058
  2. 2022Flow Matching for Generative Modelingcited by 5,702
  3. 2018Neural Ordinary Differential Equationscited by 3,779
  4. 2022Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flowcited by 3,700
  5. 2014Deep Learning Face Attributes in the Wildcited by 3,693
  6. 2015Variational Inference with Normalizing Flowscited by 2,170
  7. 2023Align your Latents: High-Resolution Video Synthesis with Latent Diffusion Modelscited by 1,476
  8. 2023Stochastic Interpolants: A Unifying Framework for Flows and Diffusionscited by 939
  9. 2023Improving and generalizing flow-based generative models with minibatch optimal transportcited by 879
  10. 2025Mean Flows for One-step Generative Modelingcited by 561
  11. 2022On Neural Differential Equationscited by 268
  12. 2025Improved Mean Flows: On the Challenges of Fastforward Generative Modelscited by 110
18 more
  1. 2025How to build a consistency model: Learning flow maps via self-distillationcited by 103
  2. 2020Interacting particle solutions of Fokker-Planck equations through gradient-log-density estimationcited by 88
  3. 2025Align Your Flow: Scaling Continuous-Time Flow Map Distillationcited by 87
  4. 2024Generator Matching: Generative modeling with arbitrary Markov processescited by 86
  5. 2021Efficient and Accurate Gradients for Neural SDEscited by 71
  6. 2023The Blessing of Randomness: SDE Beats ODE in General Diffusion-based Image Editingcited by 62
  7. 2021Smooth Normalizing Flowscited by 53
  8. 2026Meta Flow Maps enable scalable reward alignmentcited by 37
  9. 2024Stable Neural Stochastic Differential Equations in Analyzing Irregular Time Series Datacited by 36
  10. 2024Log Neural Controlled Differential Equations: The Lie Brackets Make a Differencecited by 35
  11. 2020Hypersolvers: Toward Fast Continuous-Depth Modelscited by 33
  12. 2026Diamond Maps: Efficient Reward Alignment via Stochastic Flow Mapscited by 29
  13. 2025Consistent Sampling and Simulation: Molecular Dynamics with Energy-Based Diffusion Modelscited by 23
  14. 2025FALCON: Few-step Accurate Likelihoods for Continuous Flowscited by 13
  15. 2025Neural Stochastic Flows: Solver-Free Modelling and Inference for SDE Solutionscited by 5
  16. 2026General Multimodal Protein Design Enables DNA-Encoding of Chemistrycited by 4
  17. 2024Single-seed generation of Brownian paths and integrals for adaptive and high order SDE solverscited by 3
  18. 2025Rex: A Family of Reversible Exponential (Stochastic) Runge-Kutta Solverscited by 3

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 6.

6 papers.

  1. 2026Flow-Map GRPO: Reinforcement Learning for Few-Step Flow-Map Generators via Anchored Stochastic Compositioncited by 3
  2. 2026Accelerating Diffusion Sampling via Speculative Draft Treescited by 2
  3. 2026Twisted Schr"odinger Bridge Matchingcited by 1
  4. 2026OMatG-flash: An All-Atom Flow Map with Reinforce Adjoint Matching for Scalable Materials Discoverycited by 1
  5. 2026Langevin Flow Maps: Efficient Molecular Dynamics and Transition Path Samplingcited by 0
  6. 2026Noise, Denoise, Correct: MCMC Posterior Sampling with Diffusion Priors in Three Stepscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2026Stochastic Transition-Map Distillation for Fast Probabilistic Inference
  2. 2025Test-time scaling of diffusions with flow maps
  3. 2024Flow map matching with stochastic interpolants: A mathematical framework for consistency models
  4. 2024Stochastic Sampling from Deterministic Flow Models
  5. 2026Flow Map Learning via Nongradient Vector Flow
  6. 2026Training-free score-based diffusion for parameter-dependent stochastic dynamical systems
  7. 2025The Principles of Diffusion Models
  8. 2026Variational Flow Maps: Make Some Noise for One-Step Conditional Generation