The mean-field Schrödinger bridge (MFSB) problem concerns designing a minimum-effort controller that guides a diffusion process with nonlocal interaction to reach a given distribution from another by a fixed deadline. Unlike the standard Schrödinger bridge, the dynamical constraint for MFSB is the mean-field limit of a population of interacting agents with controls. It serves as a natural model for large-scale multi-agent systems. The MFSB is computationally challenging because the nonlocal interaction makes the problem nonconvex. We propose a generalization of the Hopf-Cole transform for MFSB and, building on it, design a Sinkhorn-type recursive algorithm to solve the associated system of integro-PDEs. Under mild assumptions on the interaction potential, we discuss convergence guarantees for the proposed algorithm. We present numerical examples with repulsive and attractive interactions to illustrate the theoretical contributions.

Modern real-time systems require accurate characterization of task timing behavior to ensure predictable performance, particularly on complex hardware architectures. Existing methods, such as worst-case execution time analysis, often fail to capture the fine-grained timing behaviors of a task under varying resource contexts (e.g., an allocation of cache, memory bandwidth, and CPU frequency), which is necessary to achieve efficient resource utilization. In this paper, we introduce a novel generative profiling approach that synthesizes context-dependent, fine-grained timing profiles for real-time tasks, including those for unmeasured resource allocations. Our approach leverages a nonparametric, conditional multi-marginal Schrödinger Bridge (MSB) formulation to generate accurate execution profiles for unseen resource contexts, with maximum likelihood guarantees. We demonstrate the efficiency and effectiveness of our approach through real-world benchmarks, and showcase its practical utility in a representative case study of adaptive multicore resource allocation for real-time systems.

We present a theoretical framework that reinterprets Population Annealing (PA) through the lens of the discrete-time Schrödinger Bridge (SB) problem. We demonstrate that the heuristic reweighting step in PA is derived by analytically solving the Schrödinger system without iterative computation via instantaneous projection. In addition, we identify the thermodynamic work as the optimal control potential that solves the global variational problem on path space. This perspective unifies non-equilibrium thermodynamics with the geometric framework of optimal transport, interpreting the Jarzynski equality as a consistency condition within the Donsker-Varadhan variational principle, and elucidates the thermodynamic optimality of PA.

The Schrodinger Bridge and Bass (SBB) formulation, which jointly controls drift and volatility, is an established extension of the classical Schrodinger Bridge (SB). Building on this framework, we introduce LightSBB-M, an algorithm that computes the optimal SBB transport plan in only a few iterations. The method exploits a dual representation of the SBB objective to obtain analytic expressions for the optimal drift and volatility, and it incorporates a tunable parameter beta greater than zero that interpolates between pure drift (the Schrodinger Bridge) and pure volatility (Bass martingale transport). We show that LightSBB-M achieves the lowest 2-Wasserstein distance on synthetic datasets against state-of-the-art SB and diffusion baselines with up to 32 percent improvement. We also illustrate the generative capability of the framework on an unpaired image-to-image translation task (adult to child faces in FFHQ). These findings demonstrate that LightSBB-M provides a scalable, high-fidelity SBB solver that outperforms existing SB and diffusion baselines across both synthetic and real-world generative tasks. The code is available at https://github.com/alexouadi/LightSBB-M.

Many natural dynamic processes -- such as in vivo cellular differentiation or disease progression -- can only be observed through the lens of static sample snapshots. While challenging, reconstructing their temporal evolution to decipher underlying dynamic properties is of major interest to scientific research. Existing approaches enable data transport along a temporal axis but are poorly scalable in high dimension and require restrictive assumptions to be met. To address these issues, we propose Multi-Marginal temporal Schrödinger Bridge Matching (MMtSBM) from unpaired data, extending the theoretical guarantees and empirical efficiency of Diffusion Schrödinger Bridge Matching (arXiv:2303.16852) by deriving the Iterative Markovian Fitting algorithm to multiple marginals in a novel factorized fashion. Experiments show that MMtSBM retains theoretical properties on toy examples, achieves state-of-the-art performance on real-world datasets such as transcriptomic trajectory inference in 100 dimensions, and, for the first time, recovers couplings and dynamics in very high-dimensional image settings. Our work establishes multi-marginal Schrödinger bridges as a practical and principled approach for recovering hidden dynamics from static data.

Generative robotic motion planning requires not only the synthesis of smooth and collision-free trajectories but also feasibility across diverse tasks and dynamic constraints. Prior planning methods, both traditional and generative, often struggle to incorporate high-level semantics with low-level constraints, especially the nexus between task configurations and motion controllability. In this work, we present XFlowMP, a task-conditioned generative motion planner that models robot trajectory evolution as entropic flows bridging stochastic noises and expert demonstrations via Schrodinger bridges given the inquiry task configuration. Specifically, our method leverages Schrodinger bridges as a conditional flow matching coupled with a score function to learn motion fields with high-order dynamics while encoding start-goal configurations, enabling the generation of collision-free and dynamically-feasible motions. Through evaluations, XFlowMP achieves up to 53.79% lower maximum mean discrepancy, 36.36% smoother motions, and 39.88% lower energy consumption while comparing to the next-best baseline on the RobotPointMass benchmark, and also reducing short-horizon planning time by 11.72%. On long-horizon motions in the LASA Handwriting dataset, our method maintains the trajectories with 1.26% lower maximum mean discrepancy, 3.96% smoother, and 31.97% lower energy. We further demonstrate the practicality of our method on the Kinova Gen3 manipulator, executing planning motions and confirming its robustness in real-world settings.

Diffusion models serve as a powerful generative framework for solving inverse problems. However, they still face two key challenges: 1) the distortion-perception tradeoff, where improving perceptual quality often degrades reconstruction fidelity, and 2) the exposure bias problem, where the training-inference input mismatch leads to prediction error accumulation and reduced reconstruction quality. In this work, we propose the Regularized Schr odinger Bridge (RSB), an adaptation of Schr odinger Bridge tailored for inverse problems that addresses the above limitations. RSB employs a novel regularized training strategy that perturbs both the input states and targets, effectively mitigating exposure bias by exposing the model to simulated prediction errors and also alleviating distortion by well-designed interpolation via the posterior mean. Extensive experiments on two typical inverse problems for speech enhancement demonstrate that RSB outperforms state-of-the-art methods, significantly improving distortion metrics and effectively reducing exposure bias.

Score-based generative models have recently attracted significant attention for their ability to generate high-fidelity data by learning maps from simple Gaussian priors to complex data distributions. A natural generalization of this idea to transformations between arbitrary probability distributions leads to the Schrödinger Bridge (SB) problem. However, SB solutions rarely admit closed-form expressios and are commonly obtained through iterative stochastic simulation procedures, which are computationally intensive and can be unstable. In this work, we introduce a unified closed-form framework for representing the stochastic dynamics of SB systems. Our formulation subsumes previously known analytical solutions including the Schrödinger Föllmer process and the Gaussian SB as specific instances. Notably, the classical Gaussian SB solution, previously derived using substantially more sophisticated tools such as Riemannian geometry and generator theory, follows directly from our formulation as an immediate corollary. Leveraging this framework, we develop a simulation-free algorithm that infers SB dynamics directly from samples of the source and target distributions. We demonstrate the versatility of our approach in two settings: (i) modeling developmental trajectories in single-cell genomics and (ii) solving image restoration tasks such as inpainting and deblurring. This work opens a new direction for efficient and scalable nonlinear diffusion modeling across scientific and machine learning applications.

Predicting single-cell perturbation outcomes directly advances gene function analysis and facilitates drug candidate selection, making it a key driver of both basic and translational biomedical research. However, a major bottleneck in this task is the unpaired nature of single-cell data, as the same cell cannot be observed both before and after perturbation due to the destructive nature of sequencing. Although some neural generative transport models attempt to tackle unpaired single-cell perturbation data, they either lack explicit conditioning or depend on prior spaces for indirect distribution alignment, limiting precise perturbation modeling. In this work, we approximate Schrödinger Bridge (SB), which defines stochastic dynamic mappings recovering the entropy-regularized optimal transport (OT), to directly align the distributions of control and perturbed single-cell populations across different perturbation conditions. Unlike prior SB approximations that rely on bidirectional modeling to infer optimal source-target sample coupling, we leverage Minibatch-OT based pairing to avoid such bidirectional inference and the associated ill-posedness of defining the reverse process. This pairing directly guides bridge learning, yielding a scalable approximation to the SB. We approximate two SB models, one modeling discrete gene activation states and the other continuous expression distributions. Joint training enables accurate perturbation modeling and captures single-cell heterogeneity. Experiments on public genetic and drug perturbation datasets show that our model effectively captures heterogeneous single-cell responses and achieves state-of-the-art performance.

Adaptive treatment strategies (ATS) are sequential decision-making processes that enable personalized care by dynamically adjusting treatment decisions in response to evolving patient symptoms. While reinforcement learning (RL) offers a promising approach for optimizing ATS, its conventional online trial-and-error learning mechanism is not permissible in clinical settings due to risks of harm to patients. Offline RL tackles this limitation by learning policies exclusively from historical treatment data, but its performance is often constrained by data scarcity-a pervasive challenge in clinical domains. To overcome this, we propose Treatment Stitching (TreatStitch), a novel data augmentation framework that generates clinically valid treatment trajectories by intelligently stitching segments from existing treatment data. Specifically, TreatStitch identifies similar intermediate patient states across different trajectories and stitches their respective segments. Even when intermediate states are too dissimilar to stitch directly, TreatStitch leverages the Schrödinger bridge method to generate smooth and energy-efficient bridging trajectories that connect dissimilar states. By augmenting these synthetic trajectories into the original dataset, offline RL can learn from a more diverse dataset, thereby improving its ability to optimize ATS. Extensive experiments across multiple treatment datasets demonstrate the effectiveness of TreatStitch in enhancing offline RL performance. Furthermore, we provide a theoretical justification showing that TreatStitch maintains clinical validity by avoiding out-of-distribution transitions.