Momentum Multi-Marginal Schrödinger Bridge Matching

• URL: http://arxiv.org/abs/2506.10168v1
• Date: Wed, 11 Jun 2025 20:41:23 GMT
• Title: Momentum Multi-Marginal Schrödinger Bridge Matching
• Authors: Panagiotis Theodoropoulos, Augustinos D. Saravanos, Evangelos A. Theodorou, Guan-Horng Liu,
• Abstract summary: We introduce textbfMomentum Multi-Marginal Schr"odinger Bridge Matching (3MSBM), a novel matching framework that learns smooth measure-valued splines for systems that satisfy multiple positional constraints.<n>As a matching approach, 3MSBM learns transport maps that preserve intermediate marginals throughout training, significantly improving convergence and scalability.
• Score: 20.53138254276056
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Understanding complex systems by inferring trajectories from sparse sample snapshots is a fundamental challenge in a wide range of domains, e.g., single-cell biology, meteorology, and economics. Despite advancements in Bridge and Flow matching frameworks, current methodologies rely on pairwise interpolation between adjacent snapshots. This hinders their ability to capture long-range temporal dependencies and potentially affects the coherence of the inferred trajectories. To address these issues, we introduce \textbf{Momentum Multi-Marginal Schr\"odinger Bridge Matching (3MSBM)}, a novel matching framework that learns smooth measure-valued splines for stochastic systems that satisfy multiple positional constraints. This is achieved by lifting the dynamics to phase space and generalizing stochastic bridges to be conditioned on several points, forming a multi-marginal conditional stochastic optimal control problem. The underlying dynamics are then learned by minimizing a variational objective, having fixed the path induced by the multi-marginal conditional bridge. As a matching approach, 3MSBM learns transport maps that preserve intermediate marginals throughout training, significantly improving convergence and scalability. Extensive experimentation in a series of real-world applications validates the superior performance of 3MSBM compared to existing methods in capturing complex dynamics with temporal dependencies, opening new avenues for training matching frameworks in multi-marginal settings.

Related papers

• DMSC: Dynamic Multi-Scale Coordination Framework for Time Series Forecasting [14.176801586961286]
  Time Series Forecasting (TSF) faces persistent challenges in modeling intricate temporal dependencies across different scales.<n>We propose a novel Dynamic Multi-Scale Coordination Framework (DMSC) with Multi-Scale Patch Decomposition block (EMPD), Triad Interaction Block (TIB) and Adaptive Scale Routing MoE block (ASR-MoE)<n>EMPD is designed as a built-in component to dynamically segment sequences into hierarchical patches with exponentially scaled granularities.<n>TIB then jointly models intra-patch, inter-patch, and cross-variable dependencies within each layer's decomposed representations.
  arXiv  Detail & Related papers  (2025-08-03T13:11:52Z)
• WSM: Decay-Free Learning Rate Schedule via Checkpoint Merging for LLM Pre-training [64.0932926819307]
  We present Warmup-Stable and Merge (WSM), a framework that establishes a formal connection between learning rate decay and model merging.<n>WSM provides a unified theoretical foundation for emulating various decay strategies.<n>Our framework consistently outperforms the widely-adopted Warmup-Stable-Decay (WSD) approach across multiple benchmarks.
  arXiv  Detail & Related papers  (2025-07-23T16:02:06Z)
• FindRec: Stein-Guided Entropic Flow for Multi-Modal Sequential Recommendation [50.438552588818]
  We propose textbfFindRec (textbfFlexible unified textbfinformation textbfdisentanglement for multi-modal sequential textbfRecommendation)<n>A Stein kernel-based Integrated Information Coordination Module (IICM) theoretically guarantees distribution consistency between multimodal features and ID streams.<n>A cross-modal expert routing mechanism that adaptively filters and combines multimodal features based on their contextual relevance.
  arXiv  Detail & Related papers  (2025-07-07T04:09:45Z)
• Branched Schrödinger Bridge Matching [45.105452288011726]
  We introduce Branched Schr"odinger Bridge Matching (BranchSBM), a novel framework that learns branched Schr"odinger bridges.<n>BranchSBM parameterizes multiple time-dependent velocity fields and growth processes, enabling the representation of population-level divergence into terminal distributions.<n>We show that BranchSBM is not only more expressive but also essential for tasks involving multi-path surface navigation, modeling cell fate bifurcations from homogeneous progenitor states, and simulating diverging cellular responses to perturbations.
  arXiv  Detail & Related papers  (2025-06-10T17:29:48Z)
• GeoMM: On Geodesic Perspective for Multi-modal Learning [55.41612200877861]
  This paper introduces geodesic distance as a novel distance metric in multi-modal learning for the first time.<n>Our approach incorporates a comprehensive series of strategies to adapt geodesic distance for the current multimodal learning.
  arXiv  Detail & Related papers  (2025-05-16T13:12:41Z)
• Multi-Agent Path Finding in Continuous Spaces with Projected Diffusion Models [57.45019514036948]
  Multi-Agent Path Finding (MAPF) is a fundamental problem in robotics.<n>This work proposes a novel approach that integrates constrained optimization with diffusion models for MAPF in continuous spaces.
  arXiv  Detail & Related papers  (2024-12-23T21:27:19Z)
• Go With the Flow: Fast Diffusion for Gaussian Mixture Models [16.07896640031724]
  Schrodinger Bridges (SBs) are diffusion processes that steer in finite time, a given initial distribution to another final one while minimizing a suitable cost functional.<n>We propose an analytic parametrization of a set of feasible policies for solving low dimensional problems.<n>We showcase the potential of this approach in low-to-image problems such as image-to-image translation in the latent space of an autoencoder, learning of cellular dynamics using multi-marginal momentum SB problems and various other examples.
  arXiv  Detail & Related papers  (2024-12-12T08:40:22Z)
• Adaptive Multi-Scale Decomposition Framework for Time Series Forecasting [26.141054975797868]
  We propose a novel Adaptive Multi-Scale Decomposition (AMD) framework for time series forecasting.<n>Our framework decomposes time series into distinct temporal patterns at multiple scales, leveraging the Multi-Scale Decomposable Mixing (MDM) block.<n>Our approach effectively models both temporal and channel dependencies and utilizes autocorrelation to refine multi-scale data integration.
  arXiv  Detail & Related papers  (2024-06-06T05:27:33Z)
• Generalized Schrödinger Bridge Matching [54.171931505066]
  Generalized Schr"odinger Bridge (GSB) problem setup is prevalent in many scientific areas both within and without machine learning. We propose Generalized Schr"odinger Bridge Matching (GSBM), a new matching algorithm inspired by recent advances. We show that such a generalization can be cast as solving conditional optimal control, for which variational approximations can be used.
  arXiv  Detail & Related papers  (2023-10-03T17:42:11Z)
• A Dynamical System View of Langevin-Based Non-Convex Sampling [44.002384711340966]
  Non- sampling is a key challenge in machine learning, central to non-rate optimization in deep learning as well as to approximate its significance. Existing guarantees typically only hold for the averaged distances rather than the more desirable last-rate iterates. We develop a new framework that lifts the above issues by harnessing several tools from the theory systems.
  arXiv  Detail & Related papers  (2022-10-25T09:43:36Z)
• Fast Simultaneous Gravitational Alignment of Multiple Point Sets [82.32416743939004]
  This paper proposes a new resilient technique for simultaneous registration of multiple point sets by interpreting the latter as particle swarms rigidly moving in the mutually induced force fields. Thanks to the improved simulation with altered physical laws and acceleration of globally multiply-linked point interactions, our Multi-Body Gravitational Approach (MBGA) is robust to noise and missing data. In various experimental settings, MBGA is shown to outperform several baseline point set alignment approaches in terms of accuracy and runtime.
  arXiv  Detail & Related papers  (2021-06-21T17:59:40Z)
• Learning Salient Boundary Feature for Anchor-free Temporal Action Localization [81.55295042558409]
  Temporal action localization is an important yet challenging task in video understanding. We propose the first purely anchor-free temporal localization method. Our model includes (i) an end-to-end trainable basic predictor, (ii) a saliency-based refinement module, and (iii) several consistency constraints.
  arXiv  Detail & Related papers  (2021-03-24T12:28:32Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.