AI summaryⓘ
The authors propose a new method for generating data called Three-Body Scattering Modeling (TBSM), which uses an energy-based approach instead of typical techniques like adversarial training or autoregressive models. Their method models interactions by attracting each generated sample toward a real example while repelling it from a generated one, enabling direct supervision for a one-step generator. This approach allows efficient training with fewer comparisons per batch and achieves strong performance on image generation tasks with minimal generation steps. The authors also connect their method to existing frameworks like diffusion models and GANs, showing how energy-based scattering can guide high-dimensional generation effectively.
generative modelsenergy-based modelsThree-Body Scattering2-Wasserstein distanceone-step generationImageNetFID scoregradient flowPixelDiTlatent space modeling
Authors
Peng Sun, Zhenglin Cheng, Deyuan Liu, Jun Xie, Xinyi Shang, Tao Lin
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.