Three-Body Scattering for Generative Modeling

• URL: http://arxiv.org/abs/2607.18198v1
• Date: Mon, 20 Jul 2026 17:38:12 GMT
• Title: Three-Body Scattering for Generative Modeling
• Abstract summary: We show that a proper distributional energy can induce sample-level motion and provide direct regression supervision for a one-step generator.<n>Three-Body Scattering Modeling for generation turns the energy distance into a constant-size per-projectile interaction.<n>We provide a design map relating diffusion-related supervision, Drift-like dynamics, and GAN-like objectives.
• Score: 17.851305398372794
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $\frac12D_E^2(P_θ,Q)$. 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: https://github.com/sp12138/TBSM.

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