Multi-Objective Generative Optimization via Expected Hypervolume Fine-Tuning

Scientific discovery requires plausible designs spanning useful trade-offs among competing properties: a molecule with strong binding affinity, for example, may be difficult to synthesize. Pretrained generative models, e.g., flow and diffusion generators, provide a foundation for proposing such designs, but steering them toward high-quality, complementary trade-offs remains challenging. Inference-time search incurs high per-sample costs, while fine-tuning typically relies on fixed per-candidate rewards that do not capture how designs complement one another. We introduce Hypervolume Fine-Tuning (HVFT), which adapts a single pretrained generator to maximize the expected hypervolume of its samples while controlling departure from the pretrained distribution. Expected hypervolume jointly rewards candidate quality and collective trade-off coverage. Nonetheless, we show that it cannot be expressed as the expectation of a fixed per-candidate reward and therefore cannot be optimized directly with standard techniques. A key observation of this work is that its first variation corresponds to the expected marginal hypervolume contribution of a candidate, which yields a tractable adaptive reward via an unbiased estimator based on model samples. HVFT uses this reward to decompose the objective into a sequence of KL-proximal scalar-reward subproblems. We establish concavity, relative smoothness, and convergence guarantees for the resulting distributional procedure. Across therapeutic-peptide and molecular design tasks spanning discrete diffusion and continuous flow-matching models, HVFT achieves state-of-the-art expected hypervolume and trade-off coverage.