arXiv subjects

Byoungwoo Park

Publications and source records attributed to Byoungwoo Park.

8 recordsLinked to original sources

arXiv2026

Functional Adjoint Sampler: Scalable Sampling on Infinite Dimensional Spaces

Learning-based methods for sampling from the Gibbs distribution in finite-dimensional spaces have progressed quickly, yet theory and algorithmic design for infinite-dimensional function spaces remain limited. This gap persists despite their strong potential for sampling the paths of conditional diffusion processes, enabling efficient simulation of trajectories of diffusion processes that respect rare events or boundary constraints. In this work, we present the adjoint sampler for infinite-dimensional function spaces, a stochastic optimal control-based diffusion sampler that operates in function space and targets Gibbs-type distributions on infinite-dimensional Hilbert spaces. Our Functional Adjoint Sampler (FAS) generalizes Adjoint Sampling (Havens et al., 2025) to Hilbert spaces based on a SOC theory called stochastic maximum principle, yielding a simple and scalable matching-type objective for a functional representation. We show that FAS achieves superior transition path sampling performance across synthetic potential and real molecular systems, including Alanine Dipeptide and Chignolin.

stat.ML↗

arXiv2026

Function-Space Diffusion for Motion Planning

Diffusion-based motion planners have demonstrated strong performance in generating diverse and high-quality robot trajectories in cluttered environments with multiple feasible solutions. However, existing approaches typically operate on fixed-length waypoint sequences, making the learned model resolution-dependent, thereby preventing zero-shot generalization across resolutions. In this work, we propose Function-Space Diffusion for Motion Planning (FSD-MP), a diffusion-based motion planner that models trajectories as continuous functions and performs diffusion directly in function space, achieving discretization-invariant trajectory generation. We define a mode-wise forward process in the spectral domain, driven by Gaussian noise with a Matérn-type covariance, and parameterize the reverse process with a boundary-compatible Discrete Sine Transform-based Fourier Neural Operator (DST-FNO) that preserves start-goal constraints across resolutions. We evaluate FSD-MP on 2D point robot and 7-DoF Franka manipulator planning benchmarks. Our method achieves competitive planning performance at the training resolution and generalizes zero-shot across resolutions up to 16$\times$ higher, preserving consistent planning behavior without retraining. These results demonstrate that function-space diffusion provides an effective framework for discretization-invariant motion planning.

cs.RO↗

arXiv2026

Coarse-to-Fine Compositional Diffusion for Long-Horizon Planning

Diffusion models provide strong priors for generating structured data, but many tasks require outputs beyond the scale on which these models are typically trained. Compositional generation addresses this by composing overlapping local plans from a pretrained short-horizon prior into a long-horizon output. However, standard composition primarily enforces agreement between neighboring local plans, yielding local consistency without directly specifying the global structure of the full composition. As a result, locally compatible plans may still form an implausible route, task sequence, or temporal evolution. Existing methods improve global coherence by repeatedly propagating local consistency signals or by adding inference-time optimization, but these procedures become expensive as the number or dimensionality of local plans increases. We propose Coarse-to-Fine Compositional Diffusion (CoFi), an inference-time sampler that separates global structure formation from local detail refinement. CoFi first aligns local denoised estimates around a shared coarse structure, producing a global scaffold that captures the long-range task-level arrangement. It then diffuses this scaffold to an intermediate noise level and denoises it with the same pretrained local prior, restoring local fine structure while preserving the scaffold-induced global coherence. Across long-horizon robotic planning, panoramic image generation, and long video generation, CoFi not only improves both global coherence and local sample quality over prior compositional baselines, but also requires 2-8x fewer denoiser evaluations.

cs.RO↗

arXiv2025

Improving Constrained Language Generation via Self-Distilled Twisted Sequential Monte Carlo

Recent work has framed constrained text generation with autoregressive language models as a probabilistic inference problem. Among these, Zhao et al. (2024) introduced a promising approach based on twisted Sequential Monte Carlo, which incorporates learned twist functions and twist-induced proposals to guide the generation process. However, in constrained generation settings where the target distribution concentrates on outputs that are unlikely under the base model, learning becomes challenging due to sparse and uninformative reward signals. We show that iteratively refining the base model through self-distillation alleviates this issue by making the model progressively more aligned with the target, leading to substantial gains in generation quality.

cs.LG↗

arXiv2025

Multi-Marginal Schrödinger Bridge Matching

Understanding the continuous evolution of populations from discrete temporal snapshots is a critical research challenge, particularly in fields like developmental biology and systems medicine where longitudinal tracking of individual entities is often impossible. Such trajectory inference is vital for unraveling the mechanisms of dynamic processes. While Schrödinger Bridge (SB) offer a potent framework, their traditional application to pairwise time points can be insufficient for systems defined by multiple intermediate snapshots. This paper introduces Multi-Marginal Schrödinger Bridge Matching (MSBM), a novel algorithm specifically designed for the multi-marginal SB problem. MSBM extends iterative Markovian fitting (IMF) to effectively handle multiple marginal constraints. This technique ensures robust enforcement of all intermediate marginals while preserving the continuity of the learned global dynamics across the entire trajectory. Empirical validations on synthetic data and real-world single-cell RNA sequencing datasets demonstrate the competitive or superior performance of MSBM in capturing complex trajectories and respecting intermediate distributions, all with notable computational efficiency.

stat.ML↗

arXiv2025

Stochastic Optimal Control for Diffusion Bridges in Function Spaces

Recent advancements in diffusion models and diffusion bridges primarily focus on finite-dimensional spaces, yet many real-world problems necessitate operations in infinite-dimensional function spaces for more natural and interpretable formulations. In this paper, we present a theory of stochastic optimal control (SOC) tailored to infinite-dimensional spaces, aiming to extend diffusion-based algorithms to function spaces. Specifically, we demonstrate how Doob's $h$-transform, the fundamental tool for constructing diffusion bridges, can be derived from the SOC perspective and expanded to infinite dimensions. This expansion presents a challenge, as infinite-dimensional spaces typically lack closed-form densities. Leveraging our theory, we establish that solving the optimal control problem with a specific objective function choice is equivalent to learning diffusion-based generative models. We propose two applications: (1) learning bridges between two infinite-dimensional distributions and (2) generative models for sampling from an infinite-dimensional distribution. Our approach proves effective for diverse problems involving continuous function space representations, such as resolution-free images, time-series data, and probability density functions.

cs.LG↗

arXiv2025

Amortized Control of Continuous State Space Feynman-Kac Model for Irregular Time Series

Many real-world datasets, such as healthcare, climate, and economics, are often collected as irregular time series, which poses challenges for accurate modeling. In this paper, we propose the Amortized Control of continuous State Space Model (ACSSM) for continuous dynamical modeling of time series for irregular and discrete observations. We first present a multi-marginal Doob's $h$-transform to construct a continuous dynamical system conditioned on these irregular observations. Following this, we introduce a variational inference algorithm with a tight evidence lower bound (ELBO), leveraging stochastic optimal control (SOC) theory to approximate the intractable Doob's $h$-transform and simulate the conditioned dynamics. To improve efficiency and scalability during both training and inference, ACSSM leverages auxiliary variable to flexibly parameterize the latent dynamics and amortized control. Additionally, it incorporates a simulation-free latent dynamics framework and a transformer-based data assimilation scheme, facilitating parallel inference of the latent states and ELBO computation. Through empirical evaluations across a variety of real-world datasets, ACSSM demonstrates superior performance in tasks such as classification, regression, interpolation, and extrapolation, while maintaining computational efficiency.

stat.ML↗

arXiv2025

A Foundational Brain Dynamics Model via Stochastic Optimal Control

We introduce a foundational model for brain dynamics that utilizes stochastic optimal control (SOC) and amortized inference. Our method features a continuous-discrete state space model (SSM) that can robustly handle the intricate and noisy nature of fMRI signals. To address computational limitations, we implement an approximation strategy grounded in the SOC framework. Additionally, we present a simulation-free latent dynamics approach that employs locally linear approximations, facilitating efficient and scalable inference. For effective representation learning, we derive an Evidence Lower Bound (ELBO) from the SOC formulation, which integrates smoothly with recent advancements in self-supervised learning (SSL), thereby promoting robust and transferable representations. Pre-trained on extensive datasets such as the UKB, our model attains state-of-the-art results across a variety of downstream tasks, including demographic prediction, trait analysis, disease diagnosis, and prognosis. Moreover, evaluating on external datasets such as HCP-A, ABIDE, and ADHD200 further validates its superior abilities and resilience across different demographic and clinical distributions. Our foundational model provides a scalable and efficient approach for deciphering brain dynamics, opening up numerous applications in neuroscience.

cs.LG↗