Value Matching: Scalable and Gradient-Free Reward-Guided Flow Adaptation

Adapting large-scale flow and diffusion models to downstream tasks through reward optimization is essential for their adoption in real-world applications, including scientific discovery and image generation. While recent fine-tuning methods based on reinforcement learning and stochastic optimal control achieve compelling performance, they face severe scalability challenges due to high memory demands that scale with model complexity. In contrast, methods that disentangle reward adaptation from base model complexity, such as Classifier Guidance (CG), offer flexible control over computational resource requirements. However, CG suffers from limited reward expressivity and a train-test distribution mismatch due to its offline nature. To overcome the limitations of fine-tuning methods and CG, we propose Value Matching (VM), an online algorithm for learning the value function within an optimal control setting. VM provides tunable memory and compute demands through flexible value network complexity, supports optimization of non-differentiable rewards, and operates on-policy, which enables going beyond the data distribution to discover high-reward regions. Experimentally, we evaluate VM across image generation and molecular design tasks. We demonstrate improved stability and sample efficiency over CG and achieve comparable performance to fine-tuning approaches while requiring less than 5% of their memory usage.