Efficient One-to-many Domain Translation via Diffusive Entropic Optimal Transport

Domain translation requires a delicate balance between realism, input-output alignment, and output diversity. Entropic optimal transport (EOT) provides a principled formulation of this trade-off, but its practical use remains challenging. Directly maximizing entropy of a stochastic transport plan requires evaluating log densities of generator-induced distributions, which scales poorly with dimension. In contrast, diffusion models make density information accessible in high dimensions through noising the corresponding distributions and approximating their score functions. In this work, we introduce the diffusive entropy regularizer that measures diversity after progressively noising the conditional output distribution, making the entropy term compatible with score estimation. The resulting \textbf{Diffusive EOT} retains the main theoretical guarantees of EOT: a unique solution, controllable diversity, and convergence to unregularized OT solution in the zero-regularization limit. We introduce \textbf{DM-EOT}, a practical algorithm for approximately solving the Diffusive EOT that combines diffusion-based distribution matching with transport cost and diffusive entropy penalties. DM-EOT supports fast one-step generation and higher-fidelity diffusion-based multi-step sampling. Both variants achieve comparable or superior performance on unpaired domain translation benchmarks among one-to-many baselines with comparable inference cost and diversity.