  Recent advancements in the realm of deep generative models focus on
generating samples that satisfy multiple desired properties. However, prevalent
approaches optimize these property functions independently, thus omitting the
trade-offs among them. In addition, the property optimization is often
improperly integrated into the generative models, resulting in an unnecessary
compromise on generation quality (i.e., the quality of generated samples). To
address these issues, we formulate a constrained optimization problem. It seeks
to optimize generation quality while ensuring that generated samples reside at
the Pareto front of multiple property objectives. Such a formulation enables
the generation of samples that cannot be further improved simultaneously on the
conflicting property functions and preserves good quality of generated samples.
Building upon this formulation, we introduce the PaRetO-gUided Diffusion model
(PROUD), wherein the gradients in the denoising process are dynamically
adjusted to enhance generation quality while the generated samples adhere to
Pareto optimality. Experimental evaluations on image generation and protein
generation tasks demonstrate that our PROUD consistently maintains superior
generation quality while approaching Pareto optimality across multiple property
functions compared to various baselines.
