Generating DDPM-based Samples from Tilted Distributions

arXiv cs.LG / 4/6/2026

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Key Points

The paper studies how to generate diffusion-model (DDPM) samples from a “tilted” version of an unknown base distribution, where the tilt is controlled by a vector parameter \(\theta\in\mathbb{R}^d\).
It proposes a plug-in estimator for constructing the tilted distribution and proves it is minimax-optimal under the stated setup.
The authors derive Wasserstein-distance bounds to quantify when the generated distribution from the plug-in estimator is close to the true tilted distribution, characterizing regimes in terms of \(n\) and \(\theta\).
Under additional assumptions, they provide total-variation (TV) accuracy guarantees for running diffusion on tilted samples, and they validate the theory with extensive simulations.
The work targets practical settings—such as finance and weather/climate modeling—where moment constraints or scenario reweighting motivate sampling from tilted distributions.

Abstract

Given

n

independent samples from a

d

-dimensional probability distribution, our aim is to generate diffusion-based samples from a distribution obtained by tilting the original, where the degree of tilt is parametrized by

\theta \in \mathbb{R}^d

. We define a plug-in estimator and show that it is minimax-optimal. We develop Wasserstein bounds between the distribution of the plug-in estimator and the true distribution as a function of

n

and

\theta

, illustrating regimes where the output and the desired true distribution are close. Further, under some assumptions, we prove the TV-accuracy of running Diffusion on these tilted samples. Our theoretical results are supported by extensive simulations. Applications of our work include finance, weather and climate modelling, and many other domains, where the aim may be to generate samples from a tilted distribution that satisfies practically motivated moment constraints.