Three-Body Scattering for Generative Modeling

2026-07-20

AI Summary

Traditional generative models rely on adversarial training, predefined mappings, or autoregressive factorizations, which struggle to achieve high-quality one-step generation. This work proposes Three-Body Scattering Modeling (TBSM), introducing for the first time a three-body scattering mechanism into generative modeling: each sample is attracted by a real data source and repelled by an independent generated source, with sample motion induced by distributional energy to provide direct regression supervision for a one-step generator. The method replaces full-batch pairwise field computations with constant-scale per-sample interactions and tracks conditional expectations online to suppress field noise. Leveraging the equivalence between energy distance and 2-Wasserstein gradient flow velocity, TBSM enables efficient training in a frozen feature space. On ImageNet-256, PixelDiT-XL and latent-space DiT-XL achieve FID scores of 2.23 and 1.63, respectively, at NFE=1, demonstrating superior performance in high-dimensional one-step generation.

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.

Problem

• generative modeling
• one-step generation
• energy-based models
• high-dimensional data
• distributional learning

Innovation

• Three-Body Scattering
• One-step Generation
• Wasserstein Gradient Flow
• Energy-based Modeling
• Sample-level Supervision