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

[Submitted on 13 Jan 2026 (v1), last revised 9 Jun 2026 (this version, v2)]

View PDF HTML (experimental)

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 emph{MMD Guidance}, a training-free mechanism that augments the reverse diffusion process with gradients of the textit{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. The project code is available at this http URL.

Submission history

From: Mohammad Jalali [view email]
[v1] Tue, 13 Jan 2026 09:42:57 UTC (47,673 KB)
[v2] Tue, 9 Jun 2026 06:35:29 UTC (34,853 KB)