In flow matching, the optimal velocity is determined by the conditional endpoint mean. This turns the endpoint mean into a natural test-time control handle: condition on a reference set, and the model shifts its generative dynamics toward it. In practice, this lets us steer pretrained flow models through examples alone, without retraining or learned guidance - pointing to a broader direction: generative models that adapt through data, not parameter updates.</p>\n","updatedAt":"2026-05-18T14:56:56.285Z","author":{"_id":"65a062e0684c018bd4c16bee","avatarUrl":"https://cdn-avatars.huggingface.co/v1/production/uploads/65a062e0684c018bd4c16bee/sJ1MoRruRbRE76e3sT4-L.jpeg","fullname":"Pedro Curvo","name":"pedrocurvo","type":"user","isPro":false,"isHf":false,"isHfAdmin":false,"isMod":false,"followerCount":1,"isUserFollowing":false}},"numEdits":0,"identifiedLanguage":{"language":"en","probability":0.8709988594055176},"editors":["pedrocurvo"],"editorAvatarUrls":["https://cdn-avatars.huggingface.co/v1/production/uploads/65a062e0684c018bd4c16bee/sJ1MoRruRbRE76e3sT4-L.jpeg"],"reactions":[],"isReport":false}},{"id":"6a0bc0d6ccc8b24adbb2a964","author":{"_id":"63d3e0e8ff1384ce6c5dd17d","avatarUrl":"https://cdn-avatars.huggingface.co/v1/production/uploads/1674830754237-63d3e0e8ff1384ce6c5dd17d.jpeg","fullname":"Librarian Bot (Bot)","name":"librarian-bot","type":"user","isPro":false,"isHf":false,"isHfAdmin":false,"isMod":false,"followerCount":357,"isUserFollowing":false},"createdAt":"2026-05-19T01:45:58.000Z","type":"comment","data":{"edited":false,"hidden":false,"latest":{"raw":"This is an automated message from the [Librarian Bot](https://huggingface.co/librarian-bots). I found the following papers similar to this paper. \n\nThe following papers were recommended by the Semantic Scholar API \n\n* [P-Guide: Parameter-Efficient Prior Steering for Single-Pass CFG Inference](https://huggingface.co/papers/2605.06124) (2026)\n* [Improved techniques for fine-tuning flow models via adjoint matching: a deterministic control pipeline](https://huggingface.co/papers/2605.06583) (2026)\n* [Structured Coupling for Flow Matching](https://huggingface.co/papers/2605.07676) (2026)\n* [$h$-control: Training-Free Camera Control via Block-Conditional Gibbs Refinement](https://huggingface.co/papers/2605.11871) (2026)\n* [Efficient Adjoint Matching for Fine-tuning Diffusion Models](https://huggingface.co/papers/2605.11480) (2026)\n* [Posterior Augmented Flow Matching](https://huggingface.co/papers/2605.00825) (2026)\n* [Training-Free Refinement of Flow Matching with Divergence-based Sampling](https://huggingface.co/papers/2604.04646) (2026)\n\n\n Please give a thumbs up to this comment if you found it helpful!\n\n If you want recommendations for any Paper on Hugging Face checkout [this](https://huggingface.co/spaces/librarian-bots/recommend_similar_papers) Space\n\n You can directly ask Librarian Bot for paper recommendations by tagging it in a comment: `@librarian-bot recommend`","html":"<p>This is an automated message from the <a href=\"https://huggingface.co/librarian-bots\">Librarian Bot</a>. I found the following papers similar to this paper. </p>\n<p>The following papers were recommended by the Semantic Scholar API </p>\n<ul>\n<li><a href=\"https://huggingface.co/papers/2605.06124\">P-Guide: Parameter-Efficient Prior Steering for Single-Pass CFG Inference</a> (2026)</li>\n<li><a href=\"https://huggingface.co/papers/2605.06583\">Improved techniques for fine-tuning flow models via adjoint matching: a deterministic control pipeline</a> (2026)</li>\n<li><a href=\"https://huggingface.co/papers/2605.07676\">Structured Coupling for Flow Matching</a> (2026)</li>\n<li><a href=\"https://huggingface.co/papers/2605.11871\">$h$-control: Training-Free Camera Control via Block-Conditional Gibbs Refinement</a> (2026)</li>\n<li><a href=\"https://huggingface.co/papers/2605.11480\">Efficient Adjoint Matching for Fine-tuning Diffusion Models</a> (2026)</li>\n<li><a href=\"https://huggingface.co/papers/2605.00825\">Posterior Augmented Flow Matching</a> (2026)</li>\n<li><a href=\"https://huggingface.co/papers/2604.04646\">Training-Free Refinement of Flow Matching with Divergence-based Sampling</a> (2026)</li>\n</ul>\n<p> Please give a thumbs up to this comment if you found it helpful!</p>\n<p> If you want recommendations for any Paper on Hugging Face checkout <a href=\"https://huggingface.co/spaces/librarian-bots/recommend_similar_papers\">this</a> Space</p>\n<p> You can directly ask Librarian Bot for paper recommendations by tagging it in a comment: <code><span class=\"SVELTE_PARTIAL_HYDRATER contents\" data-target=\"UserMention\" data-props=\"{&quot;user&quot;:&quot;librarian-bot&quot;}\"><span class=\"inline-block\"><span class=\"contents\"><a href=\"/librarian-bot\">@<span class=\"underline\">librarian-bot</span></a></span> </span></span> recommend</code></p>\n","updatedAt":"2026-05-19T01:45:58.728Z","author":{"_id":"63d3e0e8ff1384ce6c5dd17d","avatarUrl":"https://cdn-avatars.huggingface.co/v1/production/uploads/1674830754237-63d3e0e8ff1384ce6c5dd17d.jpeg","fullname":"Librarian Bot (Bot)","name":"librarian-bot","type":"user","isPro":false,"isHf":false,"isHfAdmin":false,"isMod":false,"followerCount":357,"isUserFollowing":false}},"numEdits":0,"identifiedLanguage":{"language":"en","probability":0.7195661664009094},"editors":["librarian-bot"],"editorAvatarUrls":["https://cdn-avatars.huggingface.co/v1/production/uploads/1674830754237-63d3e0e8ff1384ce6c5dd17d.jpeg"],"reactions":[],"isReport":false}}],"primaryEmailConfirmed":false,"paper":{"id":"2605.10302","authors":[{"_id":"6a0b251c3049bece374a8695","name":"Pedro M. P. Curvo","hidden":false},{"_id":"6a0b251c3049bece374a8696","name":"Maksim Zhdanov","hidden":false},{"_id":"6a0b251c3049bece374a8697","name":"Floor Eijkelboom","hidden":false},{"_id":"6a0b251c3049bece374a8698","name":"Jan-Willem van de Meent","hidden":false}],"mediaUrls":["https://cdn-uploads.huggingface.co/production/uploads/65a062e0684c018bd4c16bee/yVU4HFng5QqaC86CzEE5H.gif"],"publishedAt":"2026-05-12T00:00:00.000Z","submittedOnDailyAt":"2026-05-18T00:00:00.000Z","title":"Follow the Mean: Reference-Guided Flow Matching","submittedOnDailyBy":{"_id":"65a062e0684c018bd4c16bee","avatarUrl":"https://cdn-avatars.huggingface.co/v1/production/uploads/65a062e0684c018bd4c16bee/sJ1MoRruRbRE76e3sT4-L.jpeg","isPro":false,"fullname":"Pedro Curvo","user":"pedrocurvo","type":"user","name":"pedrocurvo"},"summary":"Existing approaches to controllable generation typically rely on fine-tuning, auxiliary networks, or test-time search. We show that flow matching admits a different control interface: adaptation through examples. For deterministic interpolants, the velocity field is solely governed by a conditional endpoint mean; shifting this mean shifts the flow itself. This yields a simple principle for controllable generation: steer a pretrained model by changing the reference set it follows. We instantiate this idea in two forms. Reference-Mean Guidance is training-free: it computes a closed-form endpoint-mean correction from a reference bank and applies it to a frozen FLUX.2-klein (4B) model, enabling control of color, identity, style, and structure while keeping the prompt, seed, and weights fixed. Semi-Parametric Guidance amortizes the same idea through an explicit mean anchor and learned residual refiner, matching unconditional DiT-B/4 quality on AFHQv2 while allowing the reference set to be swapped at inference time. These results point to a broader direction: generative models that adapt through data, not parameter updates.","upvotes":1,"discussionId":"6a0b251d3049bece374a8699","projectPage":"https://pedrocurvo.com/follow-the-mean","githubRepo":"https://github.com/pedrocurvo/follow-the-mean","githubRepoAddedBy":"user","ai_summary":"Flow matching enables controllable generation through example-based adaptation via conditional endpoint mean adjustment, offering training-free and parametric guidance methods for style and content control.","ai_keywords":["flow matching","deterministic interpolants","velocity field","conditional endpoint mean","reference-Mean Guidance","Semi-Parametric Guidance","FLUX.2-klein","DiT-B/4","AFHQv2"],"githubStars":1,"organization":{"_id":"6274e45cbe455dadd1063972","name":"uva","fullname":"University of Amsterdam","avatar":"https://cdn-avatars.huggingface.co/v1/production/uploads/1651827662266-6273a78c3d70b36612a8bd9e.png"}},"canReadDatabase":false,"canManagePapers":false,"canSubmit":false,"hasHfLevelAccess":false,"upvoted":false,"upvoters":[{"_id":"65a062e0684c018bd4c16bee","avatarUrl":"https://cdn-avatars.huggingface.co/v1/production/uploads/65a062e0684c018bd4c16bee/sJ1MoRruRbRE76e3sT4-L.jpeg","isPro":false,"fullname":"Pedro Curvo","user":"pedrocurvo","type":"user"}],"acceptLanguages":["en"],"dailyPaperRank":0,"organization":{"_id":"6274e45cbe455dadd1063972","name":"uva","fullname":"University of Amsterdam","avatar":"https://cdn-avatars.huggingface.co/v1/production/uploads/1651827662266-6273a78c3d70b36612a8bd9e.png"},"markdownContentUrl":"https://huggingface.co/buckets/huggingchat/papers-content/resolve/2605/2605.10302.md"}">

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