Flow Matching Ergodic Coverage

• URL: http://arxiv.org/abs/2504.17872v1
• Date: Thu, 24 Apr 2025 18:18:35 GMT
• Title: Flow Matching Ergodic Coverage
• Authors: Max Muchen Sun, Allison Pinosky, Todd Murphey,
• Abstract summary: Existing ergodic coverage methods are constrained by the limited set of ergodic metrics available for control synthesis.<n>We propose an alternative approach to ergodic coverage based on flow matching, a technique widely used in generative inference for efficient and scalable sampling.<n>Our formulation enables alternative ergodic metrics from generative inference that overcome the limitations of existing ones.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Ergodic coverage effectively generates exploratory behaviors for embodied agents by aligning the spatial distribution of the agent's trajectory with a target distribution, where the difference between these two distributions is measured by the ergodic metric. However, existing ergodic coverage methods are constrained by the limited set of ergodic metrics available for control synthesis, fundamentally limiting their performance. In this work, we propose an alternative approach to ergodic coverage based on flow matching, a technique widely used in generative inference for efficient and scalable sampling. We formally derive the flow matching problem for ergodic coverage and show that it is equivalent to a linear quadratic regulator problem with a closed-form solution. Our formulation enables alternative ergodic metrics from generative inference that overcome the limitations of existing ones. These metrics were previously infeasible for control synthesis but can now be supported with no computational overhead. Specifically, flow matching with the Stein variational gradient flow enables control synthesis directly over the score function of the target distribution, improving robustness to the unnormalized distributions; on the other hand, flow matching with the Sinkhorn divergence flow enables an optimal transport-based ergodic metric, improving coverage performance on non-smooth distributions with irregular supports. We validate the improved performance and competitive computational efficiency of our method through comprehensive numerical benchmarks and across different nonlinear dynamics. We further demonstrate the practicality of our method through a series of drawing and erasing tasks on a Franka robot.

Related papers

• Rethinking Test-Time Training: Tilting The Latent Distribution For Few-Shot Source-Free Adaptation [3.5808917363708743]
  We study test-time adaptation of foundation models for few-shot classification under a completely frozen-model regime.<n>We propose arguably the first training-free inference method that adapts predictions to the new task by performing a change of measure over the latent embedding distribution induced by the encoder.
  arXiv  Detail & Related papers  (2026-02-02T18:17:29Z)
• Learning Straight Flows: Variational Flow Matching for Efficient Generation [36.84747986070112]
  Flow Matching has limited ability in achieving one-step generation due to its reliance on learned curved trajectories.<n>textbfS-VFM explicitly enforces trajectory straightness, ideally producing linear generation paths.
  arXiv  Detail & Related papers  (2025-11-15T22:51:58Z)
• On Geometric Structures for Policy Parameterization in Continuous Control [7.056222499095849]
  We propose a novel, computationally efficient action generation paradigm that preserves the structural benefits of operating on a unit manifold.<n>Our method decomposes the action into a deterministic directional vector and a learnable concentration, enabling efficient between the target direction and uniform noise.<n> Empirically, our method matches or exceeds state-of-the-art methods on standard continuous control benchmarks.
  arXiv  Detail & Related papers  (2025-11-11T13:32:38Z)
• Iterative Refinement of Flow Policies in Probability Space for Online Reinforcement Learning [56.47948583452555]
  We introduce the Stepwise Flow Policy (SWFP) framework, founded on the key insight that discretizing the flow matching inference process via a fixed-step Euler scheme aligns it with the variational Jordan-Kinderlehrer-Otto principle from optimal transport.<n>SWFP decomposes the global flow into a sequence of small, incremental transformations between proximate distributions.<n>This decomposition yields an efficient algorithm that fine-tunes pre-trained flows via a cascade of small flow blocks, offering significant advantages.
  arXiv  Detail & Related papers  (2025-10-17T07:43:51Z)
• Distributionally Robust Control with End-to-End Statistically Guaranteed Metric Learning [5.309590159815129]
  We propose a novel end-to-end finite-horizon Wasserstein DRC framework.<n>It integrates the learning of anisotropic Wasserstein metrics with downstream control tasks in a closed-loop manner.<n>We show that the proposed framework achieves superior closed-loop performance and robustness compared with state-of-the-art methods.
  arXiv  Detail & Related papers  (2025-10-11T13:40:49Z)
• Aligning Latent Spaces with Flow Priors [72.24305287508474]
  This paper presents a novel framework for aligning learnable latent spaces to arbitrary target distributions by leveraging flow-based generative models as priors.<n> Notably, the proposed method eliminates computationally expensive likelihood evaluations and avoids ODE solving during optimization.
  arXiv  Detail & Related papers  (2025-06-05T16:59:53Z)
• Unraveling the Connections between Flow Matching and Diffusion Probabilistic Models in Training-free Conditional Generation [7.3604864243987365]
  We propose Flow Matching-based Posterior Sampling (FMPS) to expand its application scope.<n>This correction term can be reformulated to incorporate a surrogate score function.<n>We show that FMPS achieves superior generation quality compared to existing state-of-the-art approaches.
  arXiv  Detail & Related papers  (2024-11-12T08:14:39Z)
• Optimizing Diffusion Models for Joint Trajectory Prediction and Controllable Generation [49.49868273653921]
  Diffusion models are promising for joint trajectory prediction and controllable generation in autonomous driving. We introduce Optimal Gaussian Diffusion (OGD) and Estimated Clean Manifold (ECM) Guidance. Our methodology streamlines the generative process, enabling practical applications with reduced computational overhead.
  arXiv  Detail & Related papers  (2024-08-01T17:59:59Z)
• Amortized Posterior Sampling with Diffusion Prior Distillation [55.03585818289934]
  Amortized Posterior Sampling is a novel variational inference approach for efficient posterior sampling in inverse problems.<n>Our method trains a conditional flow model to minimize the divergence between the variational distribution and the posterior distribution implicitly defined by the diffusion model.<n>Unlike existing methods, our approach is unsupervised, requires no paired training data, and is applicable to both Euclidean and non-Euclidean domains.
  arXiv  Detail & Related papers  (2024-07-25T09:53:12Z)
• Distributed Markov Chain Monte Carlo Sampling based on the Alternating Direction Method of Multipliers [143.6249073384419]
  In this paper, we propose a distributed sampling scheme based on the alternating direction method of multipliers. We provide both theoretical guarantees of our algorithm's convergence and experimental evidence of its superiority to the state-of-the-art. In simulation, we deploy our algorithm on linear and logistic regression tasks and illustrate its fast convergence compared to existing gradient-based methods.
  arXiv  Detail & Related papers  (2024-01-29T02:08:40Z)
• Ensemble Kalman Filtering Meets Gaussian Process SSM for Non-Mean-Field and Online Inference [47.460898983429374]
  We introduce an ensemble Kalman filter (EnKF) into the non-mean-field (NMF) variational inference framework to approximate the posterior distribution of the latent states. This novel marriage between EnKF and GPSSM not only eliminates the need for extensive parameterization in learning variational distributions, but also enables an interpretable, closed-form approximation of the evidence lower bound (ELBO) We demonstrate that the resulting EnKF-aided online algorithm embodies a principled objective function by ensuring data-fitting accuracy while incorporating model regularizations to mitigate overfitting.
  arXiv  Detail & Related papers  (2023-12-10T15:22:30Z)
• Flow-based Distributionally Robust Optimization [23.232731771848883]
  We present a framework, called $textttFlowDRO$, for solving flow-based distributionally robust optimization (DRO) problems with Wasserstein uncertainty sets. We aim to find continuous worst-case distribution (also called the Least Favorable Distribution, LFD) and sample from it. We demonstrate its usage in adversarial learning, distributionally robust hypothesis testing, and a new mechanism for data-driven distribution perturbation differential privacy.
  arXiv  Detail & Related papers  (2023-10-30T03:53:31Z)
• Low-Rank Tensor Completion via Novel Sparsity-Inducing Regularizers [30.920908325825668]
  To alleviate l1-norm in the low-rank tensor completion problem, non-rank surrogates/regularizers have been suggested. These regularizers are applied to nuclear-rank restoration, and efficient algorithms based on the method of multipliers are proposed.
  arXiv  Detail & Related papers  (2023-10-10T01:00:13Z)
• Observation-Guided Diffusion Probabilistic Models [41.749374023639156]
  We propose a novel diffusion-based image generation method called the observation-guided diffusion probabilistic model (OGDM) Our approach reestablishes the training objective by integrating the guidance of the observation process with the Markov chain. We demonstrate the effectiveness of our training algorithm using diverse inference techniques on strong diffusion model baselines.
  arXiv  Detail & Related papers  (2023-10-06T06:29:06Z)
• Robust probabilistic inference via a constrained transport metric [8.85031165304586]
  We offer a novel alternative by constructing an exponentially tilted empirical likelihood carefully designed to concentrate near a parametric family of distributions. The proposed approach finds applications in a wide variety of robust inference problems, where we intend to perform inference on the parameters associated with the centering distribution. We demonstrate superior performance of our methodology when compared against state-of-the-art robust Bayesian inference methods.
  arXiv  Detail & Related papers  (2023-03-17T16:10:06Z)
• Learning Sampling Distributions for Model Predictive Control [36.82905770866734]
  Sampling-based approaches to Model Predictive Control (MPC) have become a cornerstone of contemporary approaches to MPC. We propose to carry out all operations in the latent space, allowing us to take full advantage of the learned distribution. Specifically, we frame the learning problem as bi-level optimization and show how to train the controller with backpropagation-through-time.
  arXiv  Detail & Related papers  (2022-12-05T20:35:36Z)
• Improper Learning with Gradient-based Policy Optimization [62.50997487685586]
  We consider an improper reinforcement learning setting where the learner is given M base controllers for an unknown Markov Decision Process. We propose a gradient-based approach that operates over a class of improper mixtures of the controllers.
  arXiv  Detail & Related papers  (2021-02-16T14:53:55Z)
• Policy Analysis using Synthetic Controls in Continuous-Time [101.35070661471124]
  Counterfactual estimation using synthetic controls is one of the most successful recent methodological developments in causal inference. We propose a continuous-time alternative that models the latent counterfactual path explicitly using the formalism of controlled differential equations.
  arXiv  Detail & Related papers  (2021-02-02T16:07:39Z)
• Comparing Probability Distributions with Conditional Transport [63.11403041984197]
  We propose conditional transport (CT) as a new divergence and approximate it with the amortized CT (ACT) cost. ACT amortizes the computation of its conditional transport plans and comes with unbiased sample gradients that are straightforward to compute. On a wide variety of benchmark datasets generative modeling, substituting the default statistical distance of an existing generative adversarial network with ACT is shown to consistently improve the performance.
  arXiv  Detail & Related papers  (2020-12-28T05:14:22Z)
• Adaptive Correlated Monte Carlo for Contextual Categorical Sequence Generation [77.7420231319632]
  We adapt contextual generation of categorical sequences to a policy gradient estimator, which evaluates a set of correlated Monte Carlo (MC) rollouts for variance control. We also demonstrate the use of correlated MC rollouts for binary-tree softmax models, which reduce the high generation cost in large vocabulary scenarios.
  arXiv  Detail & Related papers  (2019-12-31T03:01:55Z)

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.