{
  "abstract": "Reinforcement learning (RL) post-training provides a direct way to align diffusion models with human preferences and task-specific rewards. However, current RL algorithms for diffusion models remain fragmented: reverse-trajectory methods rely on discretized likelihood ratios, whereas forward-matching methods train on reward-labeled noising versions of the rollout samples. This paper shows that these seemingly different losses arise from a single path-space principle. Starting from the regularized diffusion-RL objective, we use importance sampling between sampling SDEs to obtain an explicit policy-gradient estimator on trajectory space. The estimator contains the stochastic Itô integral underlying Flow-GRPO-type updates; we derive an equivalent variance-reduced value-gradient form that recovers the forward-matching structure of AWM and DiffusionNFT. This identifies the empirical gap between these method families as a variance-reduction effect rather than a difference in RL principle. The derivation yields a unified design space organized by value-gradient estimation, weight functions, and sampling choices. Within this space, we propose a multi-sample KDE value-gradient estimator that reuses rollout groups, together with scale-bounded weight families that retain stable existing recipes while excluding singular ones. Experiments on SD3.5-M and Qwen-Image models validate the variance-reduction explanation and show that the resulting recipe improves over prior diffusion-RL baselines.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.14430",
  "author_total": 5,
  "authors": [
    {
      "name": "Yixian Xu"
    },
    {
      "name": "Yuanrui Zhang"
    },
    {
      "name": "Shengjie Luo"
    },
    {
      "name": "Liwei Wang"
    },
    {
      "name": "Di He"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2zxe5hzcjwqkt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.14430",
  "fulltext_url": null,
  "id": "2zxe5hzcjwqkt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.14430",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.CV"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1707|Generative Adversarial Networks and Image Synthesis"
    ]
  ],
  "openalex": "W7203614358",
  "pdf_url": "https://arxiv.org/pdf/2608.14430",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2zxe5hzcjwqkt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:16Z",
      "native_id": "2608.14430",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.14430"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Designing Reinforcement Learning for Diffusion Models: A Unified Path-Space View",
  "title_text": "Designing Reinforcement Learning for Diffusion Models: A Unified Path-Space View",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:50Z",
  "url": "https://research.draconitic.com/paper/2zxe5hzcjwqkt",
  "venue": "arXiv",
  "versions": []
}