We introduce Three-Body Scattering Modeling (TBSM), a new framework for one-step generative modeling that learns a transport field from the generated distribution toward the real data distribution.</p>\n<p>Unlike GANs that rely on adversarial discrimination, diffusion models that follow predefined denoising trajectories, or distillation methods that require teacher models, TBSM learns a tracked scattering field to estimate how generated samples should move toward real samples. The learned tracker directly provides optimization guidance for the generator, enabling stable training of one-step and few-step generative models.</p>\n<p>TBSM achieves strong performance on challenging image generation benchmarks. On ImageNet-256, TBSM-trained one-step generators achieve competitive generation quality with NFE=1, including FID 2.23 with pixel-space PixelDiT-XL and FID 1.63 with latent-space DiT-XL. Beyond standard image generation, TBSM demonstrates stable training of large-scale text-to-image models with up to 20B parameters, achieving one-step and few-step generation without additional auxiliary losses.</p>\n<p>Beyond a new training algorithm, TBSM provides a new perspective for understanding the relationships among several major generative paradigms. By viewing generation through the lens of distributional transport fields, TBSM reveals connections among GANs, diffusion models, and drifting-based approaches.</p>\n<p>Here we provide:</p>\n<p>🎨 One-step generation visualizations from TBSM-trained models<br>🗺️ A design map illustrating the connections among existing generative modeling paradigms<br>🎬 An introduction video explaining the TBSM framework</p>\n<p>We hope TBSM offers a simple and scalable perspective toward efficient generative modeling.</p>\n<p><a href=\"https://cdn-uploads.huggingface.co/production/uploads/6305a4cf5054a1c5b82ae8f7/xRoK7fLhFw1_6_yoELqjz.jpeg\" rel=\"nofollow\"><img src=\"https://cdn-uploads.huggingface.co/production/uploads/6305a4cf5054a1c5b82ae8f7/xRoK7fLhFw1_6_yoELqjz.jpeg\" alt=\"samples-overview\"></a></p>\n<p><a href=\"https://cdn-uploads.huggingface.co/production/uploads/6305a4cf5054a1c5b82ae8f7/Hh0MrLIQrosO4szcBpQ4y.jpeg\" rel=\"nofollow\"><img src=\"https://cdn-uploads.huggingface.co/production/uploads/6305a4cf5054a1c5b82ae8f7/Hh0MrLIQrosO4szcBpQ4y.jpeg\" alt=\"text-to-image\"></a></p>\n<p><a href=\"https://cdn-uploads.huggingface.co/production/uploads/6305a4cf5054a1c5b82ae8f7/RNBUFFb5m4TVNI9iumyM3.jpeg\" rel=\"nofollow\"><img src=\"https://cdn-uploads.huggingface.co/production/uploads/6305a4cf5054a1c5b82ae8f7/RNBUFFb5m4TVNI9iumyM3.jpeg\" alt=\"design-map-paper\"></a></p>\n<p><video src=\"https://cdn-uploads.huggingface.co/production/uploads/6305a4cf5054a1c5b82ae8f7/PLw64JmjAp65OkPVsfpkl.mp4\" controls=\"\" class=\"max-w-full!\"></video></p>","updatedAt":"2026-07-27T07:57:38.503Z","author":{"_id":"6305a4cf5054a1c5b82ae8f7","avatarUrl":"/avatars/7138103d5b86d8b0b6cdd71e1dd4f1eb.svg","fullname":"Black Box","name":"sp12138sp","type":"user","isPro":false,"isHf":false,"isHfAdmin":false,"isMod":false,"followerCount":6,"isUserFollowing":false}},"numEdits":0,"identifiedLanguage":{"language":"en","probability":0.7621429562568665},"editors":["sp12138sp"],"editorAvatarUrls":["/avatars/7138103d5b86d8b0b6cdd71e1dd4f1eb.svg"],"reactions":[],"isReport":false}}],"primaryEmailConfirmed":false,"paper":{"id":"2607.18198","authors":[{"_id":"6a670515ab9cdf9be5794b0d","name":"Peng Sun","hidden":false},{"_id":"6a670515ab9cdf9be5794b0e","name":"Zhenglin Cheng","hidden":false},{"_id":"6a670515ab9cdf9be5794b0f","name":"Deyuan Liu","hidden":false},{"_id":"6a670515ab9cdf9be5794b10","name":"Jun Xie","hidden":false},{"_id":"6a670515ab9cdf9be5794b11","name":"Xinyi Shang","hidden":false},{"_id":"6a670515ab9cdf9be5794b12","name":"Tao Lin","hidden":false}],"mediaUrls":["https://cdn-uploads.huggingface.co/production/uploads/6305a4cf5054a1c5b82ae8f7/Cr_HoTPGGNsscRpibREgz.mp4","https://cdn-uploads.huggingface.co/production/uploads/6305a4cf5054a1c5b82ae8f7/kUagye9ifVxLvZd4knuW_.jpeg","https://cdn-uploads.huggingface.co/production/uploads/6305a4cf5054a1c5b82ae8f7/9j05EF0ID8htvnGkEwtiR.jpeg","https://cdn-uploads.huggingface.co/production/uploads/6305a4cf5054a1c5b82ae8f7/c4W9FSdeF6GI0n2qtMtrw.jpeg"],"publishedAt":"2026-07-20T00:00:00.000Z","submittedOnDailyAt":"2026-07-27T00:00:00.000Z","title":"Three-Body Scattering for Generative Modeling","submittedOnDailyBy":{"_id":"6305a4cf5054a1c5b82ae8f7","avatarUrl":"/avatars/7138103d5b86d8b0b6cdd71e1dd4f1eb.svg","isPro":false,"fullname":"Black Box","user":"sp12138sp","type":"user","name":"sp12138sp"},"summary":"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. 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Three-Body Scattering for Generative Modeling
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.
Community
We introduce Three-Body Scattering Modeling (TBSM), a new framework for one-step generative modeling that learns a transport field from the generated distribution toward the real data distribution.
Unlike GANs that rely on adversarial discrimination, diffusion models that follow predefined denoising trajectories, or distillation methods that require teacher models, TBSM learns a tracked scattering field to estimate how generated samples should move toward real samples. The learned tracker directly provides optimization guidance for the generator, enabling stable training of one-step and few-step generative models.
TBSM achieves strong performance on challenging image generation benchmarks. On ImageNet-256, TBSM-trained one-step generators achieve competitive generation quality with NFE=1, including FID 2.23 with pixel-space PixelDiT-XL and FID 1.63 with latent-space DiT-XL. Beyond standard image generation, TBSM demonstrates stable training of large-scale text-to-image models with up to 20B parameters, achieving one-step and few-step generation without additional auxiliary losses.
Beyond a new training algorithm, TBSM provides a new perspective for understanding the relationships among several major generative paradigms. By viewing generation through the lens of distributional transport fields, TBSM reveals connections among GANs, diffusion models, and drifting-based approaches.
Here we provide:
🎨 One-step generation visualizations from TBSM-trained models
🗺️ A design map illustrating the connections among existing generative modeling paradigms
🎬 An introduction video explaining the TBSM framework
We hope TBSM offers a simple and scalable perspective toward efficient generative modeling.
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Cite arxiv.org/abs/2607.18198 in a model README.md to link it from this page.
Cite arxiv.org/abs/2607.18198 in a dataset README.md to link it from this page.
Cite arxiv.org/abs/2607.18198 in a Space README.md to link it from this page.
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