--- source: arxiv source_url: https://arxiv.org/abs/2605.08078 tags: [reinforcement-learning, skill-curation, self-evolving-agents, llm-agent, skill-repo, grpo, composite-rewards] title: "Normalizing Trajectory Models" author: "" date: Mon, 11 May 2026 01:18:36 GMT review_value: 8 review_confidence: 8 review_recommendation: strong ingested: 2026-05-13 sha256: a36feaf1c05d373e0e38ce3e0f2802cfb17d1bb446e37dea875bd9c48e2e21a8 --- [2605.08078] Normalizing Trajectory Models Skip to main content [](https://www.cornell.edu/) Learn about arXiv becoming an independent nonprofit. We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors.Donate [](https://arxiv.org/IgnoreMe) [](https://arxiv.org/)>cs> arXiv:2605.08078 Help | Advanced Search Search [](https://arxiv.org/) [](https://www.cornell.edu/) GO quick links Login Help Pages About Computer Science > Computer Vision and Pattern Recognition arXiv:2605.08078 (cs) [Submitted on 8 May 2026] Title:Normalizing Trajectory Models Authors:Jiatao Gu, Tianrong Chen, Ying Shen, David Berthelot, Shuangfei Zhai, Josh Susskind View a PDF of the paper titled Normalizing Trajectory Models, by Jiatao Gu and 5 other authors View PDFHTML (experimental) > Abstract:Diffusion-based models decompose sampling into many small Gaussian denoising steps -- an assumption that breaks down when generation is compressed to a few coarse transitions. Existing few-step methods address this through distillation, consistency training, or adversarial objectives, but sacrifice the likelihood framework in the process. We introduce Normalizing Trajectory Models (NTM), which models each reverse step as an expressive conditional normalizing flow with exact likelihood training. Architecturally, NTM combines shallow invertible blocks within each step with a deep parallel predictor across the trajectory, forming an end-to-end network trainable from scratch or initializable from pretrained flow-matching models. Its exact trajectory likelihood further enables self-distillation: a lightweight denoiser trained on the model's own score produces high-quality samples in four steps. On text-to-image benchmarks, NTM matches or outperforms strong image generation baselines in just four sampling steps while uniquely retaining exact likelihood over the generative trajectory. Subjects:Computer Vision and Pattern Recognition (cs.CV); Machine Learning (cs.LG) Cite as:arXiv:2605.08078 [cs.CV] (or arXiv:2605.08078v1 [cs.CV] for this version) https://doi.org/10.48550/arXiv.2605.08078 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Jiatao Gu [view email] [v1] Fri, 8 May 2026 17:57:14 UTC (30,986 KB) [](https://arxiv.org/abs/2605.08078)Full-text links: Access Paper: View a PDF of the paper titled Normalizing Trajectory Models, by Jiatao Gu and 5 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cs.CV ") new | recent | 2026-05 Change to browse by: cs cs.LG References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... 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