MMD Guidance: Training-Free Method for Adapting Diffusion Models to Target Data Distributions
Researchers have introduced MMD Guidance, a training-free technique that steers pre-trained diffusion models toward user-specific target distributions using Maximum Mean Discrepancy during the reverse diffusion process. The method addresses a common limitation where diffusion model outputs diverge from domain-specific reference data, particularly when only a few examples are available and retraining is impractical. It offers a more direct distributional alignment approach compared to existing inference-time guidance methods that rely on surrogate objectives.
MMD Guidance is a proposed inference-time mechanism that injects gradients of the Maximum Mean Discrepancy (MMD) — a statistical measure of distributional similarity — into the reverse diffusion process of pre-trained generative models, without requiring any model retraining. The approach is designed for domain adaptation scenarios where only limited reference examples exist, exploiting MMD's known properties of low variance and reliable estimation from small datasets. The framework extends to conditional generation through prompt-aware adaptation using product kernels, and is compatible with latent diffusion models (LDMs) by operating in the latent space, improving computational efficiency. Experiments on both synthetic and real-world benchmarks are reported to show that the method achieves distributional alignment while maintaining sample fidelity. The work is positioned as an alternative to classifier-guidance and other surrogate-objective methods that do not directly optimize for target distribution matching. Code has been made publicly available, and the paper has undergone at least one revision since its initial January 2026 submission.
What's missing
Limitations such as sensitivity to kernel choice in MMD, behavior under very high-dimensional latent spaces, or failure modes with highly out-of-distribution reference sets are not discussed in the available abstract. Scalability to very large reference datasets and computational overhead relative to baselines remain open questions.
What different sources said
- arXiv cs.LGCenter
MMD Guidance: Training-Free Distribution Adaptation for Diffusion Models via Maximum Mean Discrepancy Guidance
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