[2607.18198] Three-Body Scattering for Generative Modeling

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arXiv:2607.18198 (cs)

[Submitted on 20 Jul 2026]

Title:Three-Body Scattering for Generative Modeling

Authors:Peng Sun, Zhenglin Cheng, Deyuan Liu, Jun Xie, Xinyi Shang, Tao Lin<br>View a PDF of the paper titled Three-Body Scattering for Generative Modeling, by Peng Sun and 5 other authors

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Abstract:Modern generative models typically rely on an adversarial critic, a prescribed noise-to-data path, or an autoregressive factorization. Instead, we show that a proper distributional energy can induce sample-level motion and provide direct regression supervision for a one-step generator. Three-Body Scattering Modeling (TBSM) for generation turns the energy distance into a constant-size per-projectile interaction: each projectile is attracted toward one real source and repelled from one independently generated source. Conditioned on the projectile and its condition, its expectation equals the $2$-Wasserstein gradient-flow velocity of $\frac12D_E^2(P_{\theta},Q)$. A batch of $B$ frozen-target events yields $O(B)$ sample-level losses, each using one reference for its condition instead of the minibatch-wide all-pairs field used by methods such as Drifting Models. Tracking this conditional expectation online can reduce field noise. Using scattering in frozen image features, TBSM trains one-step generators on ImageNet-256, achieving FID${}=2.23$ with pixel-space PixelDiT-XL and FID${}=1.63$ with latent-space DiT-XL at NFE${}=1$. We provide a design map relating diffusion-related supervision, Drift-like dynamics, and GAN-like objectives. These results establish tracked scattering as a route to high-dimensional one-step generation. Code: this https URL.

Comments:<br>31 pages, 5 figures, and 4 tables. Code: this https URL

Subjects:

Machine Learning (cs.LG); Computer Vision and Pattern Recognition (cs.CV)

Cite as:<br>arXiv:2607.18198 [cs.LG]

(or<br>arXiv:2607.18198v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2607.18198

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arXiv-issued DOI via DataCite (pending registration)

Submission history<br>From: Peng Sun [view email]<br>[v1]<br>Mon, 20 Jul 2026 17:38:12 UTC (6,457 KB)

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