Training-Free Distribution Adaptation for Diffusion Models via Maximum Mean Discrepancy Guidance

TL;DR

This paper introduces MMD Guidance, a training-free method that uses Maximum Mean Discrepancy to adapt pre-trained diffusion models to new target data distributions efficiently, especially useful in domain adaptation with limited data.

Contribution

It proposes a novel, training-free MMD-based guidance mechanism for diffusion models that directly aligns generated samples with target distributions without retraining.

Findings

Achieves effective distributional alignment with limited data

Preserves sample quality while adapting to new distributions

Applicable to latent diffusion models for computational efficiency

Abstract

Pre-trained diffusion models have emerged as powerful generative priors for both unconditional and conditional sample generation, yet their outputs often deviate from the characteristics of user-specific target data. Such mismatches are especially problematic in domain adaptation tasks, where only a few reference examples are available and retraining the diffusion model is infeasible. Existing inference-time guidance methods can adjust sampling trajectories, but they typically optimize surrogate objectives such as classifier likelihoods rather than directly aligning with the target distribution. We propose MMD Guidance, a training-free mechanism that augments the reverse diffusion process with gradients of the Maximum Mean Discrepancy (MMD) between generated samples and a reference dataset. MMD provides reliable distributional estimates from limited data, exhibits low variance in practice, and is efficiently differentiable, which makes it particularly well-suited for the guidance task. Our framework naturally extends to prompt-aware adaptation in conditional generation models via product kernels. Also, it can be applied with computational efficiency in latent diffusion models (LDMs), since guidance is applied in the latent space of the LDM. Experiments on synthetic and real-world benchmarks demonstrate that MMD Guidance can achieve distributional alignment while preserving sample fidelity.