mlsanityData to 7 Oct 2026

Discrete Adjoint Schr"odinger Bridge Sampler

arXiv 2602.08243 ↗First posted 9 Feb 2026stat.ML cs.LGcited by 4

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Abstract (arXiv)

Learning discrete neural samplers is challenging due to the lack of gradients and combinatorial complexity. While stochastic optimal control (SOC) and Schr"odinger bridge (SB) provide principled solutions, efficient SOC solvers like adjoint matching (AM), which excel in continuous domains, remain unexplored for discrete spaces. We bridge this gap by revealing that the core mechanism of AM is mathitstate-mathitspace~agnostic, and introduce discrete~ASBS, a unified framework that extends AM and adjoint Schr"odinger bridge sampler (ASBS) to discrete spaces. Theoretically, we analyze the optimality conditions of the discrete SB problem and its connection to SOC, identifying a necessary cyclic group structure on the state space to enable this extension. Empirically, discrete ASBS achieves competitive sample quality with significant advantages in training efficiency and scalability.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 59 of its 79 references that are in the map. First posted on arXiv 9 Feb 2026.

Builds on

59 of 79 references.

References · 59

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38 more
  1. 2024Rotary Position Embedding for Vision Transformercited by 226
  2. 2024Adjoint Matching: Fine-tuning Flow and Diffusion Generative Models with Memoryless Stochastic Optimal Controlcited by 222
  3. 2021Likelihood Training of Schr"odinger Bridge using Forward-Backward SDEs Theorycited by 216
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  9. 2025Adjoint Sampling: Highly Scalable Diffusion Samplers via Adjoint Matchingcited by 78
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  20. 2015Entropic and displacement interpolation: a computational approach using the Hilbert metriccited by 34
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  29. 2025MDNS: Masked Diffusion Neural Sampler via Stochastic Optimal Controlcited by 20
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50 most cited of 59 All 59 (JSON)

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 4.

4 papers.

  1. 2026Bridge Matching Sampler: Scalable Sampling via Generalized Fixed-Point Diffusion Matchingcited by 7
  2. 2026Adjoint Matching through the Lens of the Stochastic Maximum Principle in Optimal Controlcited by 4
  3. 2026Fixed-point neural samplers on discrete spacescited by 0
  4. 2026Cost-augmented Schr"odinger bridges on graphs are exactly solvable: a Feynman-Kac tilt replaces learned controlcited by 0