Variance-Tilted Diffusion Models for Diverse Sampling
For practitioners using diffusion models for diverse sampling (e.g., drug discovery, image generation), this provides a principled alternative to heuristic repulsive methods.
The paper introduces a variance-weighted batch distribution for diffusion models to generate diverse samples, deriving an interacting-particle sampler via Doob's h-transform that repels posterior means and moves particles to high-variance regions.
Diffusion models are typically sampled independently, even when the downstream objective is to obtain a diverse set of candidates. We introduce a variance-weighted batch distribution that favours collections of samples with large empirical spread after a prescribed linear feature map. The target is specified explicitly, and the sampler is derived as the corresponding Doob $h$-transform of independent diffusion dynamics. The resulting correction has a compact form: an interaction term that repels posterior denoised means, together with a curvature term that moves particles to the region of higher feature variance. This yields an interacting-particle sampler with a transparent probabilistic target rather than a heuristic repulsive drift.