--- source: newsletter 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" sha256: cc23da6a6d5db2bab868b32d77110302ed42b14099bd6599b84a06b035bdbaab date: 2026-05-13 review_value: 8 review_confidence: 9 review_recommendation: neutral ingested: 2026-05-16 --- Published Time: Mon, 11 May 2026 01:18:36 GMT Markdown Content: # [2605.08078] Normalizing Trajectory Models [Skip to main content](https://arxiv.org/abs/2605.08078#content) [![Image 1: Cornell University Logo](https://arxiv.org/static/browse/0.3.4/images/icons/cu/cornell-reduced-white-SMALL.svg)](https://www.cornell.edu/) [Learn about arXiv becoming an independent nonprofit.](https://tech.cornell.edu/arxiv/) We gratefully acknowledge support from the Simons Foundation, [member institutions](https://info.arxiv.org/about/ourmembers.html), and all contributors.[Donate](https://info.arxiv.org/about/donate.html) [](https://arxiv.org/IgnoreMe) [![Image 2: arxiv logo](https://arxiv.org/static/browse/0.3.4/images/arxiv-logo-one-color-white.svg)](https://arxiv.org/)>[cs](https://arxiv.org/list/cs/recent)> arXiv:2605.08078 [Help](https://info.arxiv.org/help) | [Advanced Search](https://arxiv.org/search/advanced) Search [![Image 3: arXiv logo](https://arxiv.org/static/browse/0.3.4/images/arxiv-logomark-small-white.svg)](https://arxiv.org/) [![Image 4: Cornell University Logo](https://arxiv.org/static/browse/0.3.4/images/icons/cu/cornell-reduced-white-SMALL.svg)](https://www.cornell.edu/) GO ## quick links * [Login](https://arxiv.org/login) * [Help Pages](https://info.arxiv.org/help) * [About](https://info.arxiv.org/about) # Computer Science > Computer Vision and Pattern Recognition **arXiv:2605.08078** (cs) [Submitted on 8 May 2026] # Title:Normalizing Trajectory Models Authors:[Jiatao Gu](https://arxiv.org/search/cs?searchtype=author&query=Gu,+J), [Tianrong Chen](https://arxiv.org/search/cs?searchtype=author&query=Chen,+T), [Ying Shen](https://arxiv.org/search/cs?searchtype=author&query=Shen,+Y), [David Berthelot](https://arxiv.org/search/cs?searchtype=author&query=Berthelot,+D), [Shuangfei Zhai](https://arxiv.org/search/cs?searchtype=author&query=Zhai,+S), [Josh Susskind](https://arxiv.org/search/cs?searchtype=author&query=Susskind,+J) View a PDF of the paper titled Normalizing Trajectory Models, by Jiatao Gu and 5 other authors [View PDF](https://arxiv.org/pdf/2605.08078)[HTML (experimental)](https://arxiv.org/html/2605.08078v1) > 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](https://arxiv.org/abs/2605.08078) [cs.CV] (or [arXiv:2605.08078v1](https://arxiv.org/abs/2605.08078v1) [cs.CV] for this version) [https://doi.org/10.48550/arXiv.2605.08078](https://doi.org/10.48550/arXiv.2605.08078) Focus to learn more arXiv-issued DOI via DataCite ## Submission history From: Jiatao Gu [[view email](https://arxiv.org/show-email/236bbc0d/2605.08078)] **[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](https://arxiv.org/pdf/2605.08078) * [HTML (experimental)](https://arxiv.org/html/2605.08078v1) * [TeX Source](https://arxiv.org/src/2605.08078) [view license](http://arxiv.org/licenses/nonexclusive-distrib/1.0/ "Rights to this article") ### Current browse context: cs.CV [](https://arxiv.org/prevnext?id=2605.08078&function=next&context=cs.CV "next in cs.CV (accesskey n)") [new](https://arxiv.org/list/cs.CV/new) | [recent](https://arxiv.org/list/cs.CV/recent) | [2026-05](https://arxiv.org/list/cs.CV/2026-05) Change to browse by: [cs](https://arxiv.org/abs/2605.08078?context=cs) [cs.LG](https://arxiv.org/abs/2605.08078?context=cs.LG) ### References & Citations * [NASA ADS](https://ui.adsabs.harvard.edu/abs/arXiv:2605.08078) * [Google Scholar](https://scholar.google.com/scholar_lookup?arxiv_id=2605.08078) * [Semantic Scholar](https://api.semanticscholar.org/arXiv:2605.08078) export BibTeX citation Loading... ## BibTeX formatted citation × Data provided by: [](https://arxiv.org/abs/2605.08078) ### Bookmark [![Image 5: BibSonomy](https://arxiv.org/static/browse/0.3.4/images/icons/social/bibsonomy.png)](http://www.bibsonomy.org/BibtexHandler?requTask=upload&url=https://arxiv.org/abs/2605.08078&description=Normalizing%20Trajectory%20Models "Bookmark on BibSonomy")[![Image 6: Reddit](https://arxiv.org/static/browse/0.3.4/images/icons/social/reddit.png)](https://reddit.com/submit?url=https://arxiv.org/abs/2605.08078&title=Normalizing%20Trajectory%20Models "Bookmark on Reddit") Bibliographic Tools # Bibliographic and Citation Tools - [x] Bibliographic Explorer Toggle Bibliographic Explorer _([What is the Explorer?](https://info.arxiv.org/labs/showcase.html#arxiv-bibliographic-explorer))_ - [x] Connected Papers Toggle Connected Papers _([What is Connected Papers?](https://www.connectedpapers.com/about))_ - [x] Litmaps Toggle Litmaps _([What is Litmaps?](https://www.litmaps.co/))_ - [x] scite.ai Toggle scite Smart Citations _([What are Smart Citations?](https://www.scite.ai/))_ Code, Data, Media # Code, Data and Media Associated with this Article - [x] alphaXiv Toggle alphaXiv _([What is alphaXiv?](https://alphaxiv.org/))_ - [x] Links to Code Toggle CatalyzeX Code Finder for Papers _([What is CatalyzeX?](https://www.catalyzex.com/))_ - [x] DagsHub Toggle DagsHub _([What is DagsHub?](https://dagshub.com/))_ - [x] GotitPub Toggle Gotit.pub _([What is GotitPub?](http://gotit.pub/faq))_ - [x] Huggingface Toggle Hugging Face _([What is Huggingface?](https://huggingface.co/huggingface))_ - [x] ScienceCast Toggle ScienceCast _([What is ScienceCast?](https://sciencecast.org/welcome))_ Demos # Demos - [x] Replicate Toggle Replicate _([What is Replicate?](https://replicate.com/docs/arxiv/about))_ - [x] Spaces Toggle Hugging Face Spaces _([What is Spaces?](https://huggingface.co/docs/hub/spaces))_ - [x] Spaces Toggle TXYZ.AI _([What is TXYZ.AI?](https://txyz.ai/))_ Related Papers # Recommenders and Search Tools - [x] Link to Influence Flower Influence Flower _([What are Influence Flowers?](https://influencemap.cmlab.dev/))_ - [x] Core recommender toggle CORE Recommender _([What is CORE?](https://core.ac.uk/services/recommender))_ * [Author](https://arxiv.org/abs/2605.08078) * [Venue](https://arxiv.org/abs/2605.08078) * [Institution](https://arxiv.org/abs/2605.08078) * [Topic](https://arxiv.org/abs/2605.08078) About arXivLabs # arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. 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