Source-Guided Flow Matching

2025-08-20

AI Summary

This work addresses the stability and generalization degradation caused by modifying pretrained vector fields in generative model guidance. We propose Source-Guided Flow Matching (SGFM): instead of perturbing the pretrained vector field, SGFM directly controls the source distribution to achieve guidance, reformulating guidance as controllable sampling from the source distribution. Theoretically, we prove that SGFM exactly recovers the target distribution, preserves the optimal flow-matching straight-line transport map, and—crucially—establish the first Wasserstein error bound, ensuring generation stability under approximate sampling and approximate vector fields. Empirically, SGFM demonstrates high fidelity, asymptotic unbiasedness, and task-agnostic flexibility across 2D synthetic data, image generation, and physics-informed modeling benchmarks.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Computer Vision: Generative Adversarial Networks (GANs) for Vision
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization

Abstract

Guidance of generative models is typically achieved by modifying the probability flow vector field through the addition of a guidance field. In this paper, we instead propose the Source-Guided Flow Matching (SGFM) framework, which modifies the source distribution directly while keeping the pre-trained vector field intact. This reduces the guidance problem to a well-defined problem of sampling from the source distribution. We theoretically show that SGFM recovers the desired target distribution exactly. Furthermore, we provide bounds on the Wasserstein error for the generated distribution when using an approximate sampler of the source distribution and an approximate vector field. The key benefit of our approach is that it allows the user to flexibly choose the sampling method depending on their specific problem. To illustrate this, we systematically compare different sampling methods and discuss conditions for asymptotically exact guidance. Moreover, our framework integrates well with optimal flow matching models since the straight transport map generated by the vector field is preserved. Experimental results on synthetic 2D benchmarks, image datasets, and physics-informed generative tasks demonstrate the effectiveness and flexibility of the proposed framework.

Problem

• Modifies source distribution directly for generative guidance
• Reduces guidance to sampling from source distribution
• Enables flexible sampling method choice for users

Innovation

• Modifies source distribution directly
• Keeps pre-trained vector field intact
• Allows flexible sampling method choice