# Stochastic Sampling from Deterministic Flow Models

arXiv: https://arxiv.org/abs/2410.02217 · HTML: https://mlsanity.com/paper/2410.02217/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 36 of its 46 references that are in the map.
- First posted on arXiv 3 Oct 2024.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 30 of 36)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [RePaint: Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.09865/) (2022)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformers](https://mlsanity.com/paper/2401.08740/) (2024)
- [Simple diffusion: End-to-end diffusion for high resolution images](https://mlsanity.com/paper/2301.11093/) (2023)
- [Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localization](https://mlsanity.com/paper/2308.03686/) (2023)
- [I2SB: Image-to-Image Schr"odinger Bridge](https://mlsanity.com/paper/2302.05872/) (2023)
- [A Variational Perspective on Diffusion-Based Generative Models and Score Matching](https://mlsanity.com/paper/2106.02808/) (2021)
- [Score Approximation, Estimation and Distribution Recovery of Diffusion Models on Low-Dimensional Data](https://mlsanity.com/paper/2302.07194/) (2023)
- [Inversion by Direct Iteration: An Alternative to Denoising Diffusion for Image Restoration](https://mlsanity.com/paper/2303.11435/) (2023)

## Built on by (most cited first, 18 of 18)

- [Scaling Image and Video Generation via Test-Time Evolutionary Search](https://mlsanity.com/paper/2505.17618/) (2025)
- [UniEdit-Flow: Unleashing Inversion and Editing in the Era of Flow Models](https://mlsanity.com/paper/2504.13109/) (2025)
- [Reangle-A-Video: 4D Video Generation as Video-to-Video Translation](https://mlsanity.com/paper/2503.09151/) (2025)
- [GARDO: Reinforcing Diffusion Models without Reward Hacking](https://mlsanity.com/paper/2512.24138/) (2025)
- [Scale Where It Matters: Training-Free Localized Scaling for Diffusion Models](https://mlsanity.com/paper/2511.19917/) (2025)
- [Latent Stochastic Interpolants](https://mlsanity.com/paper/2506.02276/) (2025)
- [StreamEdit: Training-Free Video Editing via Few-Step Streaming Video Generation](https://mlsanity.com/paper/2605.21466/) (2026)
- [Ani3DHuman: Photorealistic 3D Human Animation with Self-guided Stochastic Sampling](https://mlsanity.com/paper/2602.19089/) (2026)
- [Tuning Real-World Image Restoration at Inference: A Test-Time Scaling Paradigm for Flow Matching Models](https://mlsanity.com/paper/2603.22027/) (2026)
- [A Stabilized Path-Space Approach to Diffusion-Based Posterior Sampling](https://mlsanity.com/paper/2606.12710/) (2026)
- [Emyx: Fast and efficient all-atom protein generation](https://mlsanity.com/paper/2606.19377/) (2026)
- [Generalization Bounds for Flow-matching Generative Models for Intrinsically Low-dimensional Data](https://mlsanity.com/paper/2610.02663/) (2026)
- [Flow-Direct: Feedback-Efficient and Reusable Guidance for Flow Models via Non-Parametric Guidance Field](https://mlsanity.com/paper/2605.16348/) (2026)
- [Guided Flow Matching for Forward and Inverse PDE Problems with Sparse Observations: Algorithm and Theory](https://mlsanity.com/paper/2605.25509/) (2026)
- [GenSBI: Generative Methods for Simulation-Based Inference in JAX](https://mlsanity.com/paper/2605.27499/) (2026)
- [BayesFP: Posterior Estimation for Flow-Based Policies via Feynman-Kac Sampling](https://mlsanity.com/paper/2606.21014/) (2026)
- [Leveraging Inference-Time Compute for Diffusion Models via Global Scheduling of Denoising Trajectories](https://mlsanity.com/paper/2609.22867/) (2026)
- [Mean Velocity Matching: Rethinking Generative Dynamics in Diffusion Models](https://mlsanity.com/paper/2609.25444/) (2026)

## Abstract (arXiv)

Deterministic flow models, such as rectified flows, offer a general framework for learning a deterministic transport map between two distributions, realized as the vector field for an ordinary differential equation (ODE). However, they are sensitive to model estimation and discretization errors and do not permit different samples conditioned on an intermediate state, limiting their application. We present a general method to turn the underlying ODE of such flow models into a family of stochastic differential equations (SDEs) that have the same marginal distributions. This method permits us to derive families of stochastic samplers, for fixed (e.g., previously trained) deterministic flow models, that continuously span the spectrum of deterministic and stochastic sampling, given access to the flow field and the score function. Our method provides additional degrees of freedom that help alleviate the issues with the deterministic samplers and empirically outperforms them. We empirically demonstrate advantages of our method on a toy Gaussian setup and on the large scale ImageNet generation task. Further, our family of stochastic samplers provide an additional knob for controlling the diversity of generation, which we qualitatively demonstrate in our experiments.