Victor Yeom Song

Modern generative models have shown impressive capabilities in capturing the underlying distribution of complex datasets. Recent advances have leveraged score-based diffusion models as sources of synthetic data in applications like image generation, molecule discovery, DNA sequencing, and sequential decision-making, to name a few. Typically, these models are fine-tuned using reinforcement learning to optimize for a single objective. However, we propose that their expressiveness can be better exploited through multi-objective optimization. By balancing competing objectives, this approach refines model outputs, improving their alignment with both geometric and physical constraints. We aim to explore the theoretical and practical frameworks that direct generative models in a structured manner, guided by system dynamics-such as those defined by ODEs-and expert knowledge, integrated through techniques like reward modeling.