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This paper studies amortized sampling of the posterior over data, $\\mathbf{x}\\sim p^{\\rm post}(\\mathbf{x})\\propto p(\\mathbf{x})r(\\mathbf{x})$, in a model that consists of a diffusion generative model prior $p(\\mathbf{x})$ and a black-box constraint or likelihood function $r(\\mathbf{x})$. We state and prove the asymptotic correctness of a data-free learning objective, relative trajectory balance, for training a diffusion model that samples from this posterior, a problem that existing methods solve only approximately or in restricted cases. Relative trajectory balance arises from the generative flow network perspective on diffusion models, which allows the use of deep reinforcement learning techniques to improve mode coverage. Experiments illustrate the broad potential of unbiased inference of arbitrary posteriors under diffusion priors: in vision (classifier guidance), language (infilling under a discrete diffusion LLM), and multimodal data (text-to-image generation). Beyond generative modeling, we apply relative trajectory balance to the problem of continuous control with a score-based behavior prior, achieving state-of-the-art results on benchmarks in offline reinforcement learning.","url_abs":"https://arxiv.org/abs/2405.20971v2","url_pdf":"https://arxiv.org/pdf/2405.20971v2.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":"amortizing-intractable-inference-in-diffusion","repo_url":"https://github.com/gfnorg/diffusion-finetuning","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"continuous-control","task_name":"Continuous Control"},{"task_slug":"deep-reinforcement-learning","task_name":"Deep Reinforcement Learning"},{"task_slug":"image-generation","task_name":"Image Generation"},{"task_slug":"reinforcement-learning","task_name":"Reinforcement Learning"},{"task_slug":"text-to-image-generation-1","task_name":"Text to Image Generation"},{"task_slug":"text-to-image-generation","task_name":"Text-to-Image Generation"},{"task_slug":"continuous-control","task_name":"continuous-control"},{"task_slug":"reinforcement-learning-2","task_name":"reinforcement-learning"}],"methods":[{"method_slug":"diffusion","method_name":"Diffusion"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2405.20971","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2405.20971"}},"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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