mlsanityData to 7 Oct 2026

Control Consistency Losses for Diffusion Bridges

arXiv 2512.05070 ↗First posted 4 Dec 2025stat.ML cs.LGcited by 6

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Abstract (arXiv)

Simulating the conditioned dynamics of diffusion processes, given their initial and terminal states, is an important but challenging problem in the sciences. The difficulty is particularly pronounced for rare events, for which the unconditioned dynamics rarely reach the terminal state. In this work, we propose a novel approach for learning diffusion bridges based on a self-consistency property of the optimal control. The resulting algorithm learns the conditioned dynamics in an iterative online manner, and exhibits strong performance in a range of empirical settings without requiring differentiation through simulated trajectories. Beyond the diffusion bridge setting, we draw connections between our self-consistency framework and recent advances in the wider stochastic optimal control literature.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 23 of its 71 references that are in the map. First posted on arXiv 4 Dec 2025.

Builds on

23 of 71 references.

References · 23

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2021Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modelingcited by 594
  3. 2013A survey of the Schr"odinger problem and some of its connections with optimal transportcited by 286
  4. 2024Adjoint Matching: Fine-tuning Flow and Diffusion Generative Models with Memoryless Stochastic Optimal Controlcited by 222
  5. 2017Sticking the Landing: Simple, Lower-Variance Gradient Estimators for Variational Inferencecited by 97
  6. 2020Solving high-dimensional Hamilton-Jacobi-Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path spacecited by 80
  7. 2025Adjoint Sampling: Highly Scalable Diffusion Samplers via Adjoint Matchingcited by 78
  8. 2021Simulating Diffusion Bridges with Score Matchingcited by 51
  9. 2023Stochastic Optimal Control Matchingcited by 39
  10. 2022Stochastic Optimal Control for Collective Variable Free Sampling of Molecular Transition Pathscited by 36
  11. 2024Doob's Lagrangian: A Sample-Efficient Variational Approach to Transition Path Samplingcited by 25
  12. 2025Trust Region Constrained Measure Transport in Path Space for Stochastic Optimal Control and Inferencecited by 22
11 more
  1. 2023Transport meets Variational Inference: Controlled Monte Carlo Diffusionscited by 21
  2. 2025Conditioning Diffusions Using Malliavin Calculuscited by 15
  3. 2024A Taxonomy of Loss Functions for Stochastic Optimal Controlcited by 11
  4. 2024Transition Path Sampling with Improved Off-Policy Training of Diffusion Path Samplerscited by 10
  5. 2020Diffusion bridges for stochastic Hamiltonian systems and shape evolutionscited by 8
  6. 2025Non-equilibrium Annealed Adjoint Samplercited by 8
  7. 2014Simulation of multivariate diffusion bridgecited by 7
  8. 2023Differentiable Simulations for Enhanced Sampling of Rare Eventscited by 7
  9. 2020A piecewise deterministic Monte Carlo method for diffusion bridgescited by 5
  10. 2025Neural Guided Diffusion Bridgescited by 4
  11. 2025Functional Adjoint Sampler: Scalable Sampling on Infinite Dimensional Spacescited by 4

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 6.

6 papers.

  1. 2026Reinforce Adjoint Matching: Scaling RL Post-Training of Diffusion and Flow-Matching Modelscited by 17
  2. 2026Conditional Diffusion Guidance under Hard Constraint: A Stochastic Analysis Approachcited by 10
  3. 2026Discrete Adjoint Schr"odinger Bridge Samplercited by 4
  4. 2026Neural Backward Filtering Forward Guidingcited by 0
  5. 2026A Mean-Field Framework for Inference-Time Distributional Control of Diffusion Modelscited by 0
  6. 2026Sobolev Regularized Score Difference Estimation in Diffusion Modelscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2024Stochastic Optimal Control for Diffusion Bridges in Function Spaces
  2. 2024Stochastic Control for Fine-tuning Diffusion Models: Optimality, Regularity, and Convergence
  3. 2026Diffusion Controller: Framework, Algorithms and Parameterization
  4. 2025On Approaches to Building Surrogate ODE Models for Diffusion Bridges
  5. 2024Soft-constrained Schrodinger Bridge: a Stochastic Control Approach
  6. 2022An optimal control perspective on diffusion-based generative modeling
  7. 2024Schr"odinger Bridge with Quadratic State Cost is Exactly Solvable
  8. 2026Variational Test-time Optimization for Diffusion Synchronization