{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/dynamical-diffusion-learning-temporal","title":"Dynamical Diffusion: Learning Temporal Dynamics with Diffusion Models","arxiv_id":"2503.00951","date":"2025-03-02","proceeding":null,"authors":["Xingzhuo Guo","Yu Zhang","Baixu Chen","Haoran Xu","Jianmin Wang","Mingsheng Long"],"abstract":"Diffusion models have emerged as powerful generative frameworks by progressively adding noise to data through a forward process and then reversing this process to generate realistic samples. While these models have achieved strong performance across various tasks and modalities, their application to temporal predictive learning remains underexplored. Existing approaches treat predictive learning as a conditional generation problem, but often fail to fully exploit the temporal dynamics inherent in the data, leading to challenges in generating temporally coherent sequences. To address this, we introduce Dynamical Diffusion (DyDiff), a theoretically sound framework that incorporates temporally aware forward and reverse processes. Dynamical Diffusion explicitly models temporal transitions at each diffusion step, establishing dependencies on preceding states to better capture temporal dynamics. Through the reparameterization trick, Dynamical Diffusion achieves efficient training and inference similar to any standard diffusion model. Extensive experiments across scientific spatiotemporal forecasting, video prediction, and time series forecasting demonstrate that Dynamical Diffusion consistently improves performance in temporal predictive tasks, filling a crucial gap in existing methodologies. Code is available at this repository: https://github.com/thuml/dynamical-diffusion.","url_abs":"https://arxiv.org/abs/2503.00951v1","url_pdf":"https://arxiv.org/pdf/2503.00951v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"dynamical-diffusion-learning-temporal","repo_url":"https://github.com/thuml/dynamical-diffusion","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"time-series-forecasting","task_name":"Time Series Forecasting"},{"task_slug":"video-prediction","task_name":"Video Prediction"}],"methods":[{"method_slug":"aware","method_name":"AWARE"},{"method_slug":"diffusion","method_name":"Diffusion"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2503.00951","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2503.00951"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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