Distributional Multi-objective Black-box Optimization for Diffusion-model Inference-time Multi-Target Generation

TL;DR

The paper addresses how to perform multi-objective black-box optimization with diffusion models by deriving an optimal multi-target Boltzmann distribution and performing inference-time weighted resampling (IMG). This approach shifts the diffusion process toward the target distribution without retraining, enabling a diverse Pareto front in a single generation pass. The authors provide a negative log-likelihood perspective, practical implementation details, and a QMC-based method to sample preference vectors, and validate the method on diffusion-based multi-objective molecule generation where IMG outperforms strong evolutionary baselines in hypervolume and efficiency. The work offers a practical, integrable module to enhance diffusion-model-based optimization and demonstrates substantial gains in sample efficiency and front coverage, with potential wide applicability beyond molecular design.

Abstract

Diffusion models have been successful in learning complex data distributions. This capability has driven their application to high-dimensional multi-objective black-box optimization problem. Existing approaches often employ an external optimization loop, such as an evolutionary algorithm, to the diffusion model. However, these approaches treat the diffusion model as a black-box refiner, which overlooks the internal distribution transition of the diffusion generation process, limiting their efficiency. To address these challenges, we propose the Inference-time Multi-target Generation (IMG) algorithm, which optimizes the diffusion process at inference-time to generate samples that simultaneously satisfy multiple objectives. Specifically, our IMG performs weighted resampling during the diffusion generation process according to the expected aggregated multi-objective values. This weighted resampling strategy ensures the diffusion-generated samples are distributed according to our desired multi-target Boltzmann distribution. We further derive that the multi-target Boltzmann distribution has an interesting log-likelihood interpretation, where it is the optimal solution to the distributional multi-objective optimization problem. We implemented IMG for a multi-objective molecule generation task. Experiments show that IMG, requiring only a single generation pass, achieves a significantly higher hypervolume than baseline optimization algorithms that often require hundreds of diffusion generations. Notably, our algorithm can be viewed as an optimized diffusion process and can be integrated into existing methods to further improve their performance.

Figures (7)

• Figure 1: Demonstration of 100 preference vectors in 3-objective space generated by Alg \ref{['alg::GW2']} and Spoints.
• Figure 2: Comparison of hypervolume progression against the number of objective evaluations for all algorithms. Results are averaged over three runs, with dotted lines showing the hypervolume of IMG's intermediate noisy states and solid lines showing the baselines' running population. Experiment demonstrates IMG's superior performance and scalability with increasing resampling size $M$.
• Figure 3: Nine molecules generated our IMG in single diffusion inference pass.
• Figure 4: An ablation study on the IMG algorithm's hyperparameters. Left: Hypervolume plotted against different values of the coefficient parameter ($c$), Right: Hypervolume plotted against different batch sizes ($N$).
• Figure 5: A visual comparison of preference vector generation methods for $n=3$ objectives across different sample sizes ($N$). For each sample size, we compare our proposed QMC-based method (Algorithm 2) against the uniform Monte Carlo sampling method from Spoints. Our method consistently produces more evenly distributed vectors, avoiding the clustering and gaps.