Learning Conditional Source Distribution via Flow Reversal for Temporal Flow Matching

2026-10-04

AI Summary

This study addresses the limitation of standard flow matching in conditional generation, where a fixed source distribution constrains output quality. To overcome this, we propose CNP-Flow, a framework that introduces a Conditional Noise Predictor (CNP) to replace the conventional Gaussian prior. The optimal conditional source distribution is learned via inverse mapping supervision from a pretrained model. Furthermore, we design an efficient three-stage pipeline—pretraining flow matching, training the CNP, and fine-tuning flow matching—integrated with flow reversal techniques for effective optimization. Experiments demonstrate that CNP-Flow significantly enhances generation quality in video prediction and robotic motion planning tasks while achieving comparable performance with fewer function evaluations. Overall, this work establishes a flexible and efficient new paradigm for source distribution modeling in conditional flow matching.

Abstract

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

Problem

• Conditional Flow Matching
• Temporal Generation
• Source Distribution
• Flow Reversal
• Video Prediction

Innovation

• Conditional Flow Matching
• Flow Reversal
• Conditional Noise Predictor
• Temporal Generation
• Source Distribution Learning