{"paper":{"title":"One-Step Generative Modeling via Wasserstein Gradient Flows","license":"http://creativecommons.org/licenses/by/4.0/","headline":"W-Flow achieves one-step ImageNet 256x256 generation at 1.29 FID by training a neural network to compress a Wasserstein gradient flow.","cross_cats":["cs.CV","stat.ML"],"primary_cat":"cs.LG","authors_text":"Emmanuel J. Cand\\`es, Jiaqi Han, Puheng Li, Qiushan Guo, Renyuan Xu, Stefano Ermon","submitted_at":"2026-05-12T08:29:44Z","abstract_excerpt":"Diffusion models and flow-based methods have shown impressive generative capability, especially for images, but their sampling is expensive because it requires many iterative updates. We introduce W-Flow, a framework for training a generator that transforms samples from a simple reference distribution into samples from a target data distribution in a single step. This is achieved in two steps: we first define an evolution from the reference distribution to the target distribution through a Wasserstein gradient flow that minimizes an energy functional; second, we train a static neural generator"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"W-Flow sets a new state of the art for one-step ImageNet 256×256 generation, achieving 1.29 FID, with improved mode coverage and domain transfer. Compared to multi-step diffusion models with similar FID scores, our method yields approximately 100× faster sampling.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The finite-sample training dynamics converge to the continuous-time distributional dynamics under suitable assumptions. The abstract does not specify what those assumptions are or how restrictive they become for high-dimensional image data.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"W-Flow achieves state-of-the-art one-step ImageNet 256x256 generation at 1.29 FID by training a static neural network to follow a Wasserstein gradient flow that minimizes Sinkhorn divergence, delivering roughly 100x faster sampling than comparable multi-step models.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"W-Flow achieves one-step ImageNet 256x256 generation at 1.29 FID by training a neural network to compress a Wasserstein gradient flow.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"f49202fd16680ff92c1e7a0541d7d09da39a86c0e243932cbe5011af1b8c1b19"},"source":{"id":"2605.11755","kind":"arxiv","version":2},"verdict":{"id":"2f08913a-a3ad-4db0-ada8-0f78ec4869ed","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-13T07:41:20.795142Z","strongest_claim":"W-Flow sets a new state of the art for one-step ImageNet 256×256 generation, achieving 1.29 FID, with improved mode coverage and domain transfer. Compared to multi-step diffusion models with similar FID scores, our method yields approximately 100× faster sampling.","one_line_summary":"W-Flow achieves state-of-the-art one-step ImageNet 256x256 generation at 1.29 FID by training a static neural network to follow a Wasserstein gradient flow that minimizes Sinkhorn divergence, delivering roughly 100x faster sampling than comparable multi-step models.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The finite-sample training dynamics converge to the continuous-time distributional dynamics under suitable assumptions. 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