mlsanityData to 7 Oct 2026

A Unified Density Operator View of Flow Control and Merging

arXiv 2602.08012 ↗First posted 8 Feb 2026cs.LGcited by 2

On the map: Diffusion models → Diffusion and flow policies for robotics

Abstract (arXiv)

Recent progress in large-scale flow and diffusion models raised two fundamental algorithmic challenges: (i) control-based reward adaptation of pre-trained flows, and (ii) integration of multiple models, i.e., flow merging. While current approaches address them separately, we introduce a unifying probability-space framework that subsumes both as limit cases, and enables reward-guided flow merging, allowing principled, task-aware combination of multiple pre-trained flows (e.g., merging priors while maximizing drug-discovery utilities). Our formulation renders possible to express a rich family of operators over generative models densities, including intersection (e.g., to enforce safety), union (e.g., to compose diverse models), interpolation (e.g., for discovery), their reward-guided counterparts, as well as complex logical expressions via generative circuits. Next, we introduce Reward-Guided Flow Merging (RFM), a mirror-descent scheme that reduces reward-guided flow merging to a sequence of standard fine-tuning problems. Then, we provide first-of-their-kind theoretical guarantees for reward-guided and pure flow merging via RFM. Ultimately, we showcase the capabilities of the proposed method on illustrative settings providing visually interpretable insights, and apply our method to high-dimensional de-novo molecular design and low-energy conformer generation.

Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models. Builds on 44 of its 63 references that are in the map. First posted on arXiv 8 Feb 2026.

Builds on

44 of 63 references.

Closest ancestors · 5

Same direction, newest first

  1. 2024Adjoint Matching: Fine-tuning Flow and Diffusion Generative Models with Memoryless Stochastic Optimal Control13 Sep
  2. 2024Scores as Actions: a framework of fine-tuning diffusion models by continuous-time reinforcement learning12 Sep
  3. 2024Feedback Efficient Online Fine-Tuning of Diffusion Models26 Feb
  4. 2024Fine-Tuning of Continuous-Time Diffusion Models as Entropy-Regularized Control23 Feb
  5. 2023Diffusion Policy: Visuomotor Policy Learning via Action Diffusion7 Mar

Other references · 39

  1. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  2. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 8,964
  3. 2015Deep Unsupervised Learning using Nonequilibrium Thermodynamicscited by 7,005
  4. 2022Flow Matching for Generative Modelingcited by 5,426
  5. 2022LAION-5B: An open large-scale dataset for training next generation image-text modelscited by 4,131
  6. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  7. 2022DreamFusion: Text-to-3D using 2D Diffusioncited by 3,006
  8. 2023Consistency Modelscited by 1,778
  9. 2022Equivariant Diffusion for Molecule Generation in 3Dcited by 666
  10. 2023Safe RLHF: Safe Reinforcement Learning from Human Feedbackcited by 630
  11. 2016f-GAN: Training Generative Neural Samplers using Variational Divergence Minimizationcited by 504
  12. 2022DiffDock: Diffusion Steps, Twists, and Turns for Molecular Dockingcited by 307
27 more
  1. 2024Flow Matching Guide and Codecited by 291
  2. 2018Provably Efficient Maximum Entropy Explorationcited by 240
  3. 2020GEOM: Energy-annotated molecular conformations for property prediction and molecular generationcited by 238
  4. 2013Fast Computation of Wasserstein Barycenterscited by 216
  5. 2023Reduce, Reuse, Recycle: Compositional Generation with Energy-Based Diffusion Models and MCMCcited by 216
  6. 2020Variational Policy Gradient Method for Reinforcement Learning with General Utilitiescited by 108
  7. 2021Reward is enough for convex MDPscited by 82
  8. 2024Mixed Continuous and Categorical Flow Matching for 3D De Novo Molecule Generationcited by 53
  9. 2018Finding Mixed Nash Equilibria of Generative Adversarial Networkscited by 48
  10. 2024Fine-tuning of diffusion models via stochastic control: entropy regularization and beyondcited by 42
  11. 2024ET-Flow: Equivariant Flow-Matching for Molecular Conformer Generationcited by 41
  12. 2024The Superposition of Diffusion Models Using the Ito Density Estimatorcited by 36
  13. 2022The Importance of Non-Markovianity in Maximum State Entropy Explorationcited by 35
  14. 2022Mirror Descent with Relative Smoothness in Measure Spaces, with application to Sinkhorn and EMcited by 33
  15. 2022Challenging Common Assumptions in Convex Reinforcement Learningcited by 29
  16. 2020A gradient descent perspective on Sinkhorncited by 24
  17. 2022A unified stochastic approximation framework for learning in gamescited by 22
  18. 2025Temporal Difference Flowscited by 20
  19. 2023Reinforcement Learning with General Utilities: Simpler Variance Reduction and Large State-Action Spacecited by 18
  20. 2024Global Reinforcement Learning: Beyond Linear and Convex Rewards via Submodular Semi-gradient Methodscited by 15
  21. 2025Flow Density Control: Generative Optimization Beyond Entropy-Regularized Fine-Tuningcited by 15
  22. 2025Mechanisms of Projective Composition of Diffusion Modelscited by 13
  23. 2025Provable Maximum Entropy Manifold Exploration via Diffusion Modelscited by 12
  24. 2024Decouple-Then-Merge: Finetune Diffusion Models as Multi-Task Learningcited by 7
  25. 2025Hellinger-Kantorovich Gradient Flows: Global Exponential Decay of Entropy Functionalscited by 7
  26. 2024Geometric Active Exploration in Markov Decision Processes: the Benefit of Abstractioncited by 6
  27. 2024Analysis of Kernel Mirror Prox for Measure Optimizationcited by 4

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 2.

2 papers.

  1. 2026Efficient Tail-Aware Generative Optimization via Flow Model Fine-Tuningcited by 6
  2. 2026Constrained Flow Optimization via Sequential Fine Tuning for Molecular Designcited by 2

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