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Replace uniform and hand-crafted schedules with Adaptive Reparameterized Time (ART), a continuous-time control method that learns a time change by controlling the sampling clock speed, yielding principled timestep allocation via a leading-order Euler error surrogate. Introduce ART-RL as an auxiliary randomized Gaussian-policy formulation, prove equivalence to ART at optimality, derive actor–critic updates, and show experiments improve sample quality and transfer broadly without retraining.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/art-for-diffusion-sampling-continuous-time-control-and-actorcritic-learning/327466/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/art-for-diffusion-sampling-continuous-time-control-and-actorcritic-learning/327466.png","ImageObject",300,407,{"name":92,"@type":93},"Ivy","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-11","2026-09-21",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",14,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What problem does ART address in diffusion sampling?","Question",{"text":113,"@type":114},"ART addresses suboptimal timestep allocation when reverse-time dynamics are discretized on a fixed grid, where common uniform or hand-crafted schedules lack a principled optimization basis.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How does ART learn adaptive timesteps?",{"text":118,"@type":114},"ART learns a continuous-time time change by treating the sampling clock speed as a control, so a uniform grid on the learned clock induces adaptive timesteps in the original diffusion time.",{"name":120,"@type":111,"acceptedAnswer":121},"What is ART-RL and how is it related to ART?",{"text":122,"@type":114},"ART-RL turns schedule learning into a continuous-time reinforcement learning problem using randomized Gaussian policies. The paper proves ART-RL is equivalent to ART at optimality, with the mean of the optimal ART-RL Gaussian policy solving the ART control problem.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},327466,1790379584,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":140,"language":141,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":67,"update_tm":145,"read_time":146,"preview_page_count":4},549758252649,"https://ap-avatar.wpscdn.com/avatar/8000253669c5317157?_k=1778319167496531819","arXiv :2607 .02 137v2 [ cs .LG] 3 Jul 2026  \nART for Diffusion Sampling:  \nContinuous-Time Control and Actor–Critic Learning  \nYilie Huang∗ Wenpin Tang† Xun Yu Zhou‡  \nJuly 7, 2026  \nAbstract  \nWe study timestep allocation for score-based diffusion sampling, where a learned reverse-time dynamics is discretized on a finite grid. Uniform and hand-crafted schedules are standard choices, but they rely on ad hoc, fixed prescriptions and can therefore be suboptimal. To address this limitation, we propose Adaptive Reparameterized Time (ART), a continuous-time control formulation that learns a time change by treating the speed of the sampling clock as the control, so that a uniform grid on the learned clock induces adaptive timesteps in the original diffusion time. Based on a leading-order Euler error surrogate, ART provides a principled objective for allocating timesteps along the sampling trajectory. To solve this potentially high-dimensional deterministic control problem, we introduce ART-RL, an auxiliary randomized formulation with Gaussian policies that turns schedule learning into a continuous-time reinforcement learning problem. We prove that ART-RL is equivalent to ART at optimality, in the sense that the mean of the former’s optimal Gaussian policy is optimal for the latter. We further establish policy evaluation and policy improvement characterizations and derive trajectory-based moment identities that yield implementable actor–critic updates for solving ART-RL. We conduct experiments ranging from controlled low-dimensional settings to image generation, and show that ART-learned schedules, when plugged into existing diffusion samplers by changing only the timestep grid, consistently improve sample quality over strong baseline schedules at matched budgets. The learned schedules also exhibit broad generalizability with superior performances, transferring without retraining across sampling budgets, datasets, solvers, pipelines, and representation spaces.  \nKey words: generative AI, diffusion model, sampling, adaptive reparameterized time, optimal control, reinforcement learning, distillation, transfer learning  \n∗ Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong. Email: [yilie.huang@polyu.edu.hk](yilie.huang@polyu.edu.hk).  \n†Department of Industrial Engineering and Operations Research, Columbia University, New York, NY 10027, USA. Email: [wt2319@columbia.edu](wt2319@columbia.edu).  \n‡Department of Industrial Engineering and Operations Research and Data Science Institute, Columbia University, New York, NY 10027, USA. Email: [xz2574@columbia.edu](xz2574@columbia.edu).  \n1 Introduction  \nDiffusion models (Ho et al., 2020; Song and Ermon, 2019; Song et al., 2021b) generate samples by transforming noise into data, thereby producing draws from a target distribution learned from examples. They now underpin a broad range of modern generative systems, including text-to-image models such as DALL ·E 2 (Ramesh et al., 2022) and Stable Diffusion (Rombach et al., 2022), text-to-video generators such as Sora (OpenAI, 2024), Make-A-Video (Singer et al. , 2023) and Veo (Google, 2024) and, more recently, diffusion-based large language models such as Mercury (Khanna et al., 2025) and LLaDA (Nie et al., 2025) . A diffusion pipeline typically separates training from sampling: the score or denoising model is learned during pretraining, and inference generates samples by running a reverse-time dynamics with a numerical discretization. This paper focuses on the sampling stage, where one must choose a finite set of timesteps to discretize the learned reverse-time process. Because each step requires evaluating the learned model, the choice of time grids directly dictates how a fixed computational budget is spent and can substantially affect both efficiency and sample quality. Most existing approaches adopt uniform grids or hand-crafted schedules (Song et al., 2021a,b; Karras et al., 2022; Chen et al., 2023a; Lu et al.,","cbCaiidO3dzWPjxt","https://ap.wps.com/l/cbCaiidO3dzWPjxt","pdf",27851404,37,"English","# Abstract\n# Key words\n# 1 Introduction","[{\"question\":\"What problem does ART address in diffusion sampling?\",\"answer\":\"ART addresses suboptimal timestep allocation when reverse-time dynamics are discretized on a fixed grid, where common uniform or hand-crafted schedules lack a principled optimization basis.\"},{\"question\":\"How does ART learn adaptive timesteps?\",\"answer\":\"ART learns a continuous-time time change by treating the sampling clock speed as a control, so a uniform grid on the learned clock induces adaptive timesteps in the original diffusion time.\"},{\"question\":\"What is ART-RL and how is it related to ART?\",\"answer\":\"ART-RL turns schedule learning into a continuous-time reinforcement learning problem using randomized Gaussian policies. The paper proves ART-RL is equivalent to ART at optimality, with the mean of the optimal ART-RL Gaussian policy solving the ART control problem.\"}]","ART for Diffusion Sampling - Continuous-Time Control and Actor–Critic Learning | PDF",1789977262,93]