Unifying Distributional Training for One-Step Visual Generation

arXiv:2609.35763v1 Announce Type: new Abstract: \emph{Distributional training} provides collective supervision for one-step visual generation by matching real and generated features in frozen representation spaces. We introduce \emph{a unified theoretical framework} that separates distribution modeling from matching discrepancy and connects global objectives to pointwise feature updates through Wasserstein gradient flow. Under this framework, FD-Loss and Gaussian-kernel Drifting are recovered through Gaussian optimal transport and kernel-density-based KL matching, respectively. The framework motivates \textbf{MGFlow}, which models feature distributions with Gaussian mixtures at an adjustable granularity between global moments and sample-based representations. MGFlow supports both optimal transport and score-based matching, and couples mass-constrained sample assignment with paired component updates to address mode collapse that mixture expressivity alone does not resolve. On ImageNet $256\times256$, MGFlow substantially surpasses the FD-Loss baseline, achieving state-of-the-art results with \textbf{1.45} $\mathrm{FDr}^6$ on pMF-H and \textbf{1.64} on JiT-H. For text-to-image generation, MGFlow post-trains FLUX.2 [klein] 4B into a one-step generator that outperforms the original four-step model on both GenEval and PickScore. Project page: https://shihaoyang0423.github.io/MGFlow-website/

Abstract:\emph{Distributional training} provides collective supervision for one-step visual generation by matching real and generated features in frozen representation spaces. We introduce \emph{a unified theoretical framework} that separates distribution modeling from matching discrepancy and connects global objectives to pointwise feature updates through Wasserstein gradient flow. Under this framework, FD-Loss and Gaussian-kernel Drifting are recovered through Gaussian optimal transport and kernel-density-based KL matching, respectively. The framework motivates \textbf{MGFlow}, which models feature distributions with Gaussian mixtures at an adjustable granularity between global moments and sample-based representations. MGFlow supports both optimal transport and score-based matching, and couples mass-constrained sample assignment with paired component updates to address mode collapse that mixture expressivity alone does not resolve. On ImageNet $256\times256$, MGFlow substantially surpasses the FD-Loss baseline, achieving state-of-the-art results with \textbf{1.45} $\mathrm{FDr}^6$ on pMF-H and \textbf{1.64} on JiT-H. For text-to-image generation, MGFlow post-trains FLUX.2 [klein] 4B into a one-step generator that outperforms the original four-step model on both GenEval and PickScore. Project page: this https URL

Machine Learning (cs.LG)

arXiv:2609.35763 [cs.LG]

(or arXiv:2609.35763v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.35763 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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Unifying Distributional Training for One-Step Visual Generation

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