# Learning Conditional Source Distribution via Flow Reversal for Temporal Flow Matching

arXiv: https://arxiv.org/abs/2610.05349 · HTML: https://mlsanity.com/paper/2610.05349/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models.
- Builds on 46 of its 53 references that are in the map.
- First posted on arXiv 4 Oct 2026.

## Placed in

- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)

## Builds on (most cited first, 30 of 46)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Latte: Latent Diffusion Transformer for Video Generation](https://mlsanity.com/paper/2401.03048/) (2024)
- [CLEVRER: CoLlision Events for Video REpresentation and Reasoning](https://mlsanity.com/paper/1910.01442/) (2019)
- [MAGVIT: Masked Generative Video Transformer](https://mlsanity.com/paper/2212.05199/) (2022)
- [VideoFusion: Decomposed Diffusion Models for High-Quality Video Generation](https://mlsanity.com/paper/2303.08320/) (2023)
- [MCVD: Masked Conditional Video Diffusion for Prediction, Generation, and Interpolation](https://mlsanity.com/paper/2205.09853/) (2022)
- [Preserve Your Own Correlation: A Noise Prior for Video Diffusion Models](https://mlsanity.com/paper/2305.10474/) (2023)
- [Multisample Flow Matching: Straightening Flows with Minibatch Couplings](https://mlsanity.com/paper/2304.14772/) (2023)
- [Learning Blind Video Temporal Consistency](https://mlsanity.com/paper/1808.00449/) (2018)
- [Diffusion Probabilistic Modeling for Video Generation](https://mlsanity.com/paper/2203.09481/) (2022)
- [Steering Your Diffusion Policy with Latent Space Reinforcement Learning](https://mlsanity.com/paper/2506.15799/) (2025)
- [Motion Planning Diffusion: Learning and Planning of Robot Motions with Diffusion Models](https://mlsanity.com/paper/2308.01557/) (2023)
- [FILM: Frame Interpolation for Large Motion](https://mlsanity.com/paper/2202.04901/) (2022)
- [iVideoGPT: Interactive VideoGPTs are Scalable World Models](https://mlsanity.com/paper/2405.15223/) (2024)
- [Self-Supervised Visual Planning with Temporal Skip Connections](https://mlsanity.com/paper/1710.05268/) (2017)
- [Diffusion Models for Video Prediction and Infilling](https://mlsanity.com/paper/2206.07696/) (2022)
- [CADS: Unleashing the Diversity of Diffusion Models through Condition-Annealed Sampling](https://mlsanity.com/paper/2310.17347/) (2023)
- [ReNO: Enhancing One-step Text-to-Image Models through Reward-based Noise Optimization](https://mlsanity.com/paper/2406.04312/) (2024)
- [Go-with-the-Flow: Motion-Controllable Video Diffusion Models Using Real-Time Warped Noise](https://mlsanity.com/paper/2501.08331/) (2025)
- [Stochastic Latent Residual Video Prediction](https://mlsanity.com/paper/2002.09219/) (2020)

## Abstract (arXiv)

We introduce CNP-Flow, a flow matching framework for temporal generation that learns conditional source distributions through flow reversal. Whereas standard conditional flow matching (FM) incorporates conditioning through the vector field and draws source samples from a standard Gaussian, CNP-Flow uses a conditional noise predictor (CNP) to produce an isotropic Gaussian source for each temporal condition. The CNP is supervised by source samples obtained through flow reversal, which maps observed targets backward through a pretrained FM model. A three-stage pipeline pretrains the FM model, trains the CNP, and fine-tunes the FM model using the learned source distribution, while preserving the FM backbone architecture. Across video prediction, video interpolation, and 7-DoF Franka robot motion planning, CNP-Flow consistently improves generation quality. It also matches baseline performance with fewer function evaluations. Project page: https://embodiedai-ntu.github.io/cnpflow