Histogram-constrained Image Generation

Di!usion models have emerged as a dominant paradigm ingenerative modeling, enabling high-fidelity sampling from complex datadistributions. Despite impressive capabilities, controlling di!usion mod-els to produce outputs aligned with user intent remains an open chal-lenge, especially when balancing global coherence with local precision.Existing control mechanisms vary in the granularity of their conditioningsignals. For example, textual prompts guide generation globally throughhigh-level semantics, while ControlNet-like approaches secure precise lo-cal structure via dense conditions. In this work, we introduce Histogram-constrained Image Generation (HIG), a novel control mechanism thatfalls into the middle ground of control granularity. Our framework en-forces user-specified distributional constraints (e.g., color histograms orlatent token distributions) during the generation process with exact pre-cision. We model such control as an optimal transport (OT) problemand apply explicit guidance transformations during sampling, therebydriving the di!usion trajectory to align with the desired histogram. Wedemonstrate the versatility of HIG across diverse applications, includingconstrained generation via color/latent histograms and high-capacity in-formation embedding through histogram-level encoding. Our findings un-derscore the promise of distributional control, a flexible and interpretablecontrol scheme that is fully compatible with existing control mechanisms,diversifying the hybrid strategies for controllable image generation. Ourproject page is available at: https://maps-research.github.io/hig/.