Amortized Moment Matching Boosts Visual Generation Quality

This research introduces amortized moment matching (AMFD), a novel approach for visual generation that leverages neural networks to learn data moments as distributional training signals. By projecting diffusion denoisers through polynomial functions, the framework can explicitly identify data moments up to a certain order. A key instantiation, the Amortized Fréchet Distance (AMFD) loss, offers a more robust and scalable alternative to traditional Fréchet Distance (FD) loss, which relies on explicit marginal moment calculations. AMFD dynamically learns conditional moments through an alternating, matrix-free optimization pipeline, making it suitable for high-dimensional data. When applied to global representation features, AMFD acts as a powerful post-training objective, outperforming FD baselines and achieving superior one-step generation on ImageNet. Crucially, for text-to-image generation, AMFD's condition-aware nature leads to substantial improvements in instruction-following capabilities, enabling one-step models to surpass multi-step teachers on benchmarks like GenEval while matching performance on PickScore.