Manifold-Aligned Generative Transport

• URL: http://arxiv.org/abs/2602.19600v1
• Date: Mon, 23 Feb 2026 08:42:40 GMT
• Title: Manifold-Aligned Generative Transport
• Authors: Xinyu Tian, Xiaotong Shen,
• Abstract summary: We propose a flow-like generator that learns a one-shot, manifold-aligned transport from a low-dimensional base distribution to the data space.<n>We empirically improve fidelity and manifold concentration across synthetic and benchmark datasets while sampling substantially faster than diffusion models.
• Score: 11.857867207010981
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: High-dimensional generative modeling is fundamentally a manifold-learning problem: real data concentrate near a low-dimensional structure embedded in the ambient space. Effective generators must therefore balance support fidelity -- placing probability mass near the data manifold -- with sampling efficiency. Diffusion models often capture near-manifold structure but require many iterative denoising steps and can leak off-support; normalizing flows sample in one pass but are limited by invertibility and dimension preservation. We propose MAGT (Manifold-Aligned Generative Transport), a flow-like generator that learns a one-shot, manifold-aligned transport from a low-dimensional base distribution to the data space. Training is performed at a fixed Gaussian smoothing level, where the score is well-defined and numerically stable. We approximate this fixed-level score using a finite set of latent anchor points with self-normalized importance sampling, yielding a tractable objective. MAGT samples in a single forward pass, concentrates probability near the learned support, and induces an intrinsic density with respect to the manifold volume measure, enabling principled likelihood evaluation for generated samples. We establish finite-sample Wasserstein bounds linking smoothing level and score-approximation accuracy to generative fidelity, and empirically improve fidelity and manifold concentration across synthetic and benchmark datasets while sampling substantially faster than diffusion models.

Related papers

• Flow Matching is Adaptive to Manifold Structures [32.55405572762157]
  Flow matching is a simulation-based alternative to diffusion-based generative modeling.<n>We show how flow matching adapts to data geometry and circumvents the curse of dimensionality.
  arXiv  Detail & Related papers  (2026-02-25T23:52:32Z)
• Efficient Sampling with Discrete Diffusion Models: Sharp and Adaptive Guarantees [9.180350432640912]
  We study the sampling efficiency of score-based discrete diffusion models under a continuous-time Markov chain (CTMC) formulation.<n>For uniform discrete diffusion, we show that the $$-leaping algorithm achieves an complexity of order $tilde O(d/varepsilon)$.<n>For masking discrete diffusion, we introduce a modified $$-leaping sampler whose convergence rate is governed by an intrinsic information-theoretic quantity.
  arXiv  Detail & Related papers  (2026-02-16T18:48:17Z)
• Rethinking Refinement: Correcting Generative Bias without Noise Injection [7.28668585578288]
  Generative models, including diffusion and flow-based models, often exhibit systematic biases that degrade sample quality.<n>We show that effective bias correction can be achieved as a post-hoc procedure, without noise injection or multi-step resampling.
  arXiv  Detail & Related papers  (2026-01-29T02:34:08Z)
• Diffusion Model-Based Posterior Sampling in Full Waveform Inversion [3.2800968305157205]
  posterior sampling directly on observed seismic shot records is rarely practical at the field scale.<n>Our approach couples diffusion-based posterior sampling with simultaneous-source waveform inversion data.<n>Our method achieves lower model error and better data fit at a substantially reduced computational cost.
  arXiv  Detail & Related papers  (2025-12-14T18:34:12Z)
• Multimodal Atmospheric Super-Resolution With Deep Generative Models [1.9367648935513015]
  Score-based diffusion modeling is a generative machine learning algorithm that can be used to sample from complex distributions.<n>In this article, we apply such a concept to the super-resolution of a high-dimensional dynamical system, given the real-time availability of low-resolution and experimentally observed sparse sensor measurements.
  arXiv  Detail & Related papers  (2025-06-28T06:47:09Z)
• On the Wasserstein Convergence and Straightness of Rectified Flow [54.580605276017096]
  Rectified Flow (RF) is a generative model that aims to learn straight flow trajectories from noise to data.<n>We provide a theoretical analysis of the Wasserstein distance between the sampling distribution of RF and the target distribution.<n>We present general conditions guaranteeing uniqueness and straightness of 1-RF, which is in line with previous empirical findings.
  arXiv  Detail & Related papers  (2024-10-19T02:36:11Z)
• Convergence of Score-Based Discrete Diffusion Models: A Discrete-Time Analysis [56.442307356162864]
  We study the theoretical aspects of score-based discrete diffusion models under the Continuous Time Markov Chain (CTMC) framework.<n>We introduce a discrete-time sampling algorithm in the general state space $[S]d$ that utilizes score estimators at predefined time points.<n>Our convergence analysis employs a Girsanov-based method and establishes key properties of the discrete score function.
  arXiv  Detail & Related papers  (2024-10-03T09:07:13Z)
• Boosting Diffusion Models with Moving Average Sampling in Frequency Domain [101.43824674873508]
  Diffusion models rely on the current sample to denoise the next one, possibly resulting in denoising instability. In this paper, we reinterpret the iterative denoising process as model optimization and leverage a moving average mechanism to ensemble all the prior samples. We name the complete approach "Moving Average Sampling in Frequency domain (MASF)"
  arXiv  Detail & Related papers  (2024-03-26T16:57:55Z)
• Score-based generative models learn manifold-like structures with constrained mixing [2.843124313496295]
  How do score-based generative models learn the data distribution supported on a low-dimensional manifold? We investigate the score model of a trained SBM through its linear approximations and subspaces spanned by local feature vectors. We find that the learned vector field mixes samples by a non-conservative field within the manifold, although it denoises with normal projections as if there is an energy function in off-manifold directions.
  arXiv  Detail & Related papers  (2023-11-16T15:15:15Z)
• Diffusion Generative Flow Samplers: Improving learning signals through partial trajectory optimization [87.21285093582446]
  Diffusion Generative Flow Samplers (DGFS) is a sampling-based framework where the learning process can be tractably broken down into short partial trajectory segments. Our method takes inspiration from the theory developed for generative flow networks (GFlowNets)
  arXiv  Detail & Related papers  (2023-10-04T09:39:05Z)
• ManiFlow: Implicitly Representing Manifolds with Normalizing Flows [145.9820993054072]
  Normalizing Flows (NFs) are flexible explicit generative models that have been shown to accurately model complex real-world data distributions. We propose an optimization objective that recovers the most likely point on the manifold given a sample from the perturbed distribution. Finally, we focus on 3D point clouds for which we utilize the explicit nature of NFs, i.e. surface normals extracted from the gradient of the log-likelihood and the log-likelihood itself.
  arXiv  Detail & Related papers  (2022-08-18T16:07:59Z)
• Nonlinear Isometric Manifold Learning for Injective Normalizing Flows [58.720142291102135]
  We use isometries to separate manifold learning and density estimation. We also employ autoencoders to design embeddings with explicit inverses that do not distort the probability distribution.
  arXiv  Detail & Related papers  (2022-03-08T08:57:43Z)

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.