Flow Density Control: Generative Optimization Beyond Entropy-Regularized Fine-Tuning

We introduce Flow Density Control (FDC), an algorithm for fine-tuning flow and diffusion models to optimize general utilities beyond average rewards — including risk-averse and novelty-seeking objectives, diversity measures, and experiment design — with priors preserved via divergences beyond KL such as optimal transport distances. FDC reduces this complex problem to a sequence of simpler standard fine-tuning tasks and comes with convergence guarantees via mirror flows. We validate it on text-to-image and molecular design tasks.