[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-86403-en":3,"doc-seo-86403-105":30,"detail-sidebar-cat-0-en-105":83},{"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":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},86403,1649267921044,"Ava Thompson","https://us-avatar.wpscdn.com/avatar/1800007509477c92dfb?_k=1782875107921204101",8,"Research & Report","Eulerian Motion Guidance Robust Image Animation via Bidirectional Geometric Consistency","Recent advancements in image animation employ diffusion models to transform static images into video-like sequences. Existing controllable frameworks often use Lagrangian motion guidance, estimating optical flow relative to the initial frame, which suffers from error accumulation and supervision sparsity as time grows. This work introduces Eulerian motion guidance using adjacent-frame motion fields for short temporal hops, enabling parallel training and bounded-error supervision. A bidirectional geometric consistency mechanism applies forward-backward cycle checks to mask occluded regions and prevent drift artifacts.","Eulerian Motion Guidance: Robust Image Animation via Bidirectional Geometric Consistency  \nThong Nguyen* Khoi M. Le Cong-Duy Nguyen Luu Anh Tuan See-Kiong Ng Chunyan Miao  \nNational University of Singapore, Singapore  \nNanyang Technological University, Singapore  \nCentre for AI Research, VinUniversity, Vietnam  \n[thong.nguyen@u.nus.edu](thong.nguyen@u.nus.edu)  \narXiv :2605 .06280v5 [ cs .CV] 12 Jul 2026  \nAbstract  \nRecent advancements in image animation have utilized diffusion models to breathe life into static images. However, existing controllable frameworks typically rely on Lagrangian motion guidance, where optical flow is estimated relative to the initial frame. This paper revisits the same optical-flow primitive through a more local supervision design: we use adjacent-frame Eulerian motion fields to guide generation, where the motion signal always describes a short temporal hop. This shift enables parallelized training and provides bounded-error supervision throughout the generation process. To mitigate the drift artifacts common in adjacent frame generation, we introduce a Bidirectional Geometric Consistency mechanism, which computes a forward-backward cycle check to mathematically identify and mask occluded regions, preventing the model from learning incorrect warping objectives. Extensive experiments demonstrate that our approach accelerates training, preserves temporal coherence, and reduces dynamic artifacts compared to reference-based baselines. The code, model, and data have been made available [at nguyentthong.github.io/eulerian](at nguyentthong.github.io/eulerian).  \nCCS Concepts  \n• Computing methodologies → Motion capture; Procedural animation; • Theory of computation → Theory and algorithms for application domains.  \nKeywords  \nImage Animation, Motion Guidance, Geometric Consistency  \n1 Introduction  \nThe pursuit of “bringing images to life” has long been a fascination in computer vision, evolving from early Generative Adversarial Network (GAN)-based approaches [29] to recent controllable diffusion models [12, 43] . While current Image-to-Video (I2V) frameworks such as Stable Video Diffusion [2] and Lumiere [1] can generate plausible short clips, ensuring robust long-term temporal consistency under complex motion remains a formidable challenge. The core difficulty lies in maintaining the identity and structure of the initial image while adhering to complex motion dynamics overtime.  \nExisting methods [19, 25, 32] address this by integrating explicit motion control into frozen diffusion models. However, these approaches predominantly adopt a Lagrangian motion formulation, where optical flow is computed relative to the initial reference frame [8] . While conceptually simple, we identify two inherent structural  \n*  \nCorresponding author.  \nvulnerabilities in this reference-anchored paradigm that make it highly susceptible to error accumulation. First, as the timestep increases, the displacement magnitude grows, often violating the brightness constancy assumptions inherent in optical flow estimation [28] and leading to increasingly noisy supervisory signals. Second, supervisory sparsity: as objects move or rotate, the valid correspondence area between the initial frame and the current frame decays exponentially due to occlusions, leaving the model hallucinating in unseen regions without guidance.  \nTo mitigate these limitations, we propose a shift from Lagrangianbased to Eulerian-based Motion Guidance. Instead of tracking pixels relative to the start, we model motion as a dense field of transitions between consecutive frames. We provide a theoretical framework demonstrating how this formulation keeps optical flow estimates within the reliable, short-range regime of estimators, effectively bounding the per-step supervisory error. Moreover, this adjacent formulation allows for a parallelized batched flow computation strategy that minimizes sequential training overhead.  \nHowever, while Eulerian motion guidance p","cbCaiqTBysZrMBum","https://ap.wps.com/l/cbCaiqTBysZrMBum","pdf",1707617,3,1,11,"English","en",105,"# Introduction\n# Related Work\n## Controllable Video Generation","[{\"question\":\"What is the purpose of Bidirectional Geometric Consistency?\",\"answer\":\"It performs a forward-backward cycle check to derive an occlusion mask that filters unreliable gradients in dis-occluded regions, reducing shimmering or ghosting artifacts.\"}]",1784211527,28,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":78,"head_meta":80,"extra_data":82,"updated_unix":28},"eulerian-motion-guidance-robust-image-animation-via-bidirectional-geometric-consistency","",{"@graph":36,"@context":77},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":20},"https://docshare.wps.com/document/research-report/",{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/eulerian-motion-guidance-robust-image-animation-via-bidirectional-geometric-consistency/86403/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-27","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71],{"name":72,"@type":73,"acceptedAnswer":74},"What is the purpose of Bidirectional Geometric Consistency?","Question",{"text":75,"@type":76},"It performs a forward-backward cycle check to derive an occlusion mask that filters unreliable gradients in dis-occluded regions, reducing shimmering or ghosting artifacts.","Answer","https://schema.org",{"og:url":51,"og:type":79,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":81,"canonical":51},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":84},[85,89,93,97,102,107,112,115,120,123,127],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":86,"show_sort_weight":87,"slug":88},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":90,"show_sort_weight":91,"slug":92},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Exam",70,"exam",{"id":98,"doc_module":4,"doc_module_name":46,"category_name":99,"show_sort_weight":100,"slug":101},5,"Comic",60,"comic",{"id":103,"doc_module":4,"doc_module_name":46,"category_name":104,"show_sort_weight":105,"slug":106},6,"Technology",50,"technology",{"id":108,"doc_module":4,"doc_module_name":46,"category_name":109,"show_sort_weight":110,"slug":111},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":113,"slug":114},30,"research-report",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":46,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":128,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":98,"slug":130},19,"General","general"]