[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84887-en":3,"doc-seo-84887-105":29,"detail-sidebar-cat-0-en-105":90},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},84887,8796095461610,"Oliver","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",8,"Research & Report","x-Prediction Is All You Need Training-Free Accelerated Generation via Endpoint Decodability","Diffusion and flow matching models generate high-quality samples but their ODE samplers often require tens to hundreds of neural function evaluations (NFEs). This makes additional acceleration difficult for released checkpoints because typical speedups rely on retraining, distillation, or trajectory redesign. The work introduces endpoint decodability from x-prediction: affine probability paths enable an intermediate state and its velocity to decode a clean x0 via a closed-form MMSE estimator E[x0|xt]. Based on this, Truncated Jump Sampling (TJS) stops early and returns decoded x0, reducing NFEs by 20–70% with near-matched quality across multiple benchmarks.","x-Prediction Is All You Need:  \nTraining-Free Accelerated Generation via Endpoint Decodability  \nXin Peng 1 Ang Gao 1 ∗  \n1 School of Physical Science and Technology,  \nBeijing University of Posts and Telecommunications, Beijing, China[anggao@bupt.edu.cn](anggao@bupt.edu.cn)  \narXiv :2607 .06 1 14v2 [ cs .LG] 11 Jul 2026  \nAbstract  \nDiffusion and flow matching models generate high-quality samples, but their ODE samplers often need tens to hundreds of neural function evaluations (NFEs) . This remains a practical challenge for released checkpoints, since many accelerators require additional design choices and training cost through retraining, distillation, or trajectory redesign. We investigate a different route based on x-prediction. During sampling, standard affine probability paths already expose x0 information: an intermediate state and its path velocity determine a principled estimate of the clean sample. We formalize this property as endpoint decodability and show that the decoder is the minimum-MSE estimator E[x0 | xt] under the usual ℓ2 objective. This yields Truncated Jump Sampling (TJS): stop the ODE at an early-exit time t∗ and return the decoded x0 . TJS requires no retraining, distillation, or architecture change. Across SDXL, SD3.5M, Z-Image-Turbo, and three class-conditional benchmarks, it reduces NFEs by 20–70% with near-matched quality. The analysis also shows why endpoint prediction can work without straightening the trajectory, providing inference acceleration without trajectory redesign.  \nIntroduction  \nDiffusion models (Ho, Jain, and Abbeel 2020; Song et al. 2021; Nichol and Dhariwal 2021) and flow matching (Lipman et al. 2023; Albergo and Vanden-Eijnden 2023; Liu, Gong, and qiang liu 2023) produce stunning images but require tens to hundreds of neural function evaluations (NFEs) per sample (Rombach et al. 2022; Esser et al. 2024; BlackForest-Labs 2024; Peebles and Xie 2023) . Reducing this cost is a central challenge in generative modeling.  \nThe field has responded with a range of solutions—Rectified Flow (Liu, Gong, and qiang liu 2023), distillation (progressive (Salimans and Ho 2022), consistencybased (Song et al. 2023; Luo et al. 2023; Zheng et al. 2024), bootstrapping (Gu et al. 2023)), advanced solvers (?Lu et al. 2025; Zheng et al. 2023), and training-time scheduling (Chenet al. 2026)—all effective at reducing NFEs, all requiring changes to the trajectory, model, or training recipe. No existing approach achieves acceleration purely by modifying inference.  \n∗Corresponding author  \nThis complexity has a real and growing cost. The community has produced an enormous library of pretrained checkpoints—SDXL alone has thousands of fine-tuned variants on CivitAI and Hugging Face (Podell et al. 2023; Esseret al. 2024; Black-Forest-Labs 2024; Rombach et al. 2022; Peebles and Xie 2023) . While fast ODE solvers (DPMSolver, UniPC) can reduce the step count, further acceleration without retraining remains an open practical challenge.  \nThe field would benefit from a training-free acceleration strategy that works on models as they are, not as they could be after retraining.  \nThere is a simpler path, hiding in plain sight within the training objective itself. Diffusion and flow matching models are trained to predict x0 at every timestep. During inference, the model thus produces a valid x0 estimate at every intermediate step—and these estimates improve as integration proceeds. Once good enough, why continue? For diffusion models, DDIM (Song, Meng, andErmon 2021) already computes xˆ0 internally, but to our knowledge no prior work has systematically studied early-stopping and outputting it as a terminal inference strategy, nor provided theoretical justification for when and why this works. For flow matching, no such counterpart exists. We fill both gaps. We term this property endpoint decodability: for non-degenerate affine paths, the intermediate state and path velocity recover x0 through a closed-form decoder, wh","cbCaitrl1dEvocDp","https://ap.wps.com/l/cbCaitrl1dEvocDp","pdf",8149568,1,31,"English","en",105,"# Abstract\n# Introduction\n## Endpoint Decodability and Truncated Jump Sampling\n## Contributions\n### Principle and Theory\n### Algorithm\n### Experiments","[{\"question\":\"What is endpoint decodability in this work?\",\"answer\":\"Endpoint decodability states that for non-degenerate affine probability paths, the intermediate state xt together with its path velocity determines x0 through a closed-form decoder. Under the standard ℓ2 objective, this decoder is the MMSE-optimal estimator E[x0|xt].\"},{\"question\":\"How does Truncated Jump Sampling (TJS) accelerate generation?\",\"answer\":\"TJS uses early exit in ODE sampling: it stops at an intermediate time t* and outputs the decoded x0 instead of continuing integration. This achieves training-free acceleration without modifying the model or the inference architecture.\"},{\"question\":\"Does TJS require retraining, distillation, or architecture changes?\",\"answer\":\"No. The method is compatible with existing pretrained checkpoints and does not require retraining, distillation, or architecture changes. It can work with any ODE solver, noise schedule, CFG scale, and distillation method.\"}]",1784199025,78,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":85,"head_meta":87,"extra_data":89,"updated_unix":27},"x-prediction-is-all-you-need-training-free-accelerated-generation-via-endpoint-decodability","",{"@graph":35,"@context":84},[36,53,67],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/x-prediction-is-all-you-need-training-free-accelerated-generation-via-endpoint-decodability/84887/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":61,"encodingFormat":60,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-16",true,{"@type":64,"interactionType":65,"userInteractionCount":4},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"What is endpoint decodability in this work?","Question",{"text":74,"@type":75},"Endpoint decodability states that for non-degenerate affine probability paths, the intermediate state xt together with its path velocity determines x0 through a closed-form decoder. Under the standard ℓ2 objective, this decoder is the MMSE-optimal estimator E[x0|xt].","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"How does Truncated Jump Sampling (TJS) accelerate generation?",{"text":79,"@type":75},"TJS uses early exit in ODE sampling: it stops at an intermediate time t* and outputs the decoded x0 instead of continuing integration. This achieves training-free acceleration without modifying the model or the inference architecture.",{"name":81,"@type":72,"acceptedAnswer":82},"Does TJS require retraining, distillation, or architecture changes?",{"text":83,"@type":75},"No. The method is compatible with existing pretrained checkpoints and does not require retraining, distillation, or architecture changes. 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