Theoretical Foundation of Flow-Based Time Series Generation: Provable Approximation, Generalization, and Efficiency

• URL: http://arxiv.org/abs/2503.14076v1
• Date: Tue, 18 Mar 2025 09:53:48 GMT
• Title: Theoretical Foundation of Flow-Based Time Series Generation: Provable Approximation, Generalization, and Efficiency
• Authors: Jiangxuan Long, Zhao Song, Chiwun Yang,
• Abstract summary: This paper presents the first theoretical framework from the perspective of flow-based generative models.<n>By assuming a general data model, the fitting of the flow-based generative models is confirmed to converge to arbitrary error under the universal approximation of Diffusion Transformer (DiT)
• Score: 7.578147116161996
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Recent studies suggest utilizing generative models instead of traditional auto-regressive algorithms for time series forecasting (TSF) tasks. These non-auto-regressive approaches involving different generative methods, including GAN, Diffusion, and Flow Matching for time series, have empirically demonstrated high-quality generation capability and accuracy. However, we still lack an appropriate understanding of how it processes approximation and generalization. This paper presents the first theoretical framework from the perspective of flow-based generative models to relieve the knowledge of limitations. In particular, we provide our insights with strict guarantees from three perspectives: $\textbf{Approximation}$, $\textbf{Generalization}$ and $\textbf{Efficiency}$. In detail, our analysis achieves the contributions as follows: $\bullet$ By assuming a general data model, the fitting of the flow-based generative models is confirmed to converge to arbitrary error under the universal approximation of Diffusion Transformer (DiT). $\bullet$ Introducing a polynomial-based regularization for flow matching, the generalization error thus be bounded since the generalization of polynomial approximation. $\bullet$ The sampling for generation is considered as an optimization process, we demonstrate its fast convergence with updating standard first-order gradient descent of some objective.

Related papers

• Inference Acceleration of Autoregressive Normalizing Flows by Selective Jacobi Decoding [12.338918067455436]
  Normalizing flows are promising generative models with advantages such as theoretical rigor, analytical log-likelihood, and end-to-end training.<n>Recent advancements utilize autoregressive modeling, significantly enhancing expressive power and generation quality.<n>We propose a selective Jacobi decoding (SeJD) strategy that accelerates autoregressive inference through parallel iterative optimization.
  arXiv  Detail & Related papers  (2025-05-30T16:53:15Z)
• Theoretical Guarantees for High Order Trajectory Refinement in Generative Flows [40.884514919698596]
  Flow matching has emerged as a powerful framework for generative modeling. We prove that higher-order flow matching preserves worst case optimality as a distribution estimator.
  arXiv  Detail & Related papers  (2025-03-12T05:07:07Z)
• Preconditioned Inexact Stochastic ADMM for Deep Model [35.37705488695026]
  This paper develops an algorithm, PISA, which enables scalable parallel computing and supports various second-moment schemes.<n>Grounded in rigorous theoretical guarantees, the algorithm converges under the sole assumption of Lipschitz of the gradient.<n> Comprehensive experimental evaluations for or fine-tuning diverse FMs, including vision models, large language models, reinforcement learning models, generative adversarial networks, and recurrent neural networks, demonstrate its superior numerical performance compared to various state-of-the-art Directions.
  arXiv  Detail & Related papers  (2025-02-15T12:28:51Z)
• Fast Solvers for Discrete Diffusion Models: Theory and Applications of High-Order Algorithms [31.42317398879432]
  Current inference approaches mainly fall into two categories: exact simulation and approximate methods such as $tau$-leaping. In this work, we advance the latter category by tailoring the first extension of high-order numerical inference schemes to discrete diffusion models. We rigorously analyze the proposed schemes and establish the second-order accuracy of the $theta$-trapezoidal method in KL divergence.
  arXiv  Detail & Related papers  (2025-02-01T00:25:21Z)
• A Unified Analysis for Finite Weight Averaging [50.75116992029417]
  Averaging iterations of Gradient Descent (SGD) have achieved empirical success in training deep learning models, such as Weight Averaging (SWA), Exponential Moving Average (EMA), and LAtest Weight Averaging (LAWA) In this paper, we generalize LAWA as Finite Weight Averaging (FWA) and explain their advantages compared to SGD from the perspective of optimization and generalization.
  arXiv  Detail & Related papers  (2024-11-20T10:08:22Z)
• Flow matching achieves almost minimax optimal convergence [50.38891696297888]
  Flow matching (FM) has gained significant attention as a simulation-free generative model. This paper discusses the convergence properties of FM for large sample size under the $p$-Wasserstein distance. We establish that FM can achieve an almost minimax optimal convergence rate for $1 leq p leq 2$, presenting the first theoretical evidence that FM can reach convergence rates comparable to those of diffusion models.
  arXiv  Detail & Related papers  (2024-05-31T14:54:51Z)
• Scaling and renormalization in high-dimensional regression [72.59731158970894]
  This paper presents a succinct derivation of the training and generalization performance of a variety of high-dimensional ridge regression models. We provide an introduction and review of recent results on these topics, aimed at readers with backgrounds in physics and deep learning.
  arXiv  Detail & Related papers  (2024-05-01T15:59:00Z)
• Analysis of Bootstrap and Subsampling in High-dimensional Regularized Regression [29.57766164934947]
  We investigate popular resampling methods for estimating the uncertainty of statistical models. We provide a tight description of the biases and variances estimated by these methods in the context of generalized linear models.
  arXiv  Detail & Related papers  (2024-02-21T08:50:33Z)
• Guided Flows for Generative Modeling and Decision Making [55.42634941614435]
  We show that Guided Flows significantly improves the sample quality in conditional image generation and zero-shot text synthesis-to-speech. Notably, we are first to apply flow models for plan generation in the offline reinforcement learning setting ax speedup in compared to diffusion models.
  arXiv  Detail & Related papers  (2023-11-22T15:07:59Z)
• PROMISE: Preconditioned Stochastic Optimization Methods by Incorporating Scalable Curvature Estimates [17.777466668123886]
  We introduce PROMISE ($textbfPr$econditioned $textbfO$ptimization $textbfM$ethods by $textbfI$ncorporating $textbfS$calable Curvature $textbfE$stimates), a suite of sketching-based preconditioned gradient algorithms. PROMISE includes preconditioned versions of SVRG, SAGA, and Katyusha.
  arXiv  Detail & Related papers  (2023-09-05T07:49:10Z)
• Towards Faster Non-Asymptotic Convergence for Diffusion-Based Generative Models [49.81937966106691]
  We develop a suite of non-asymptotic theory towards understanding the data generation process of diffusion models. In contrast to prior works, our theory is developed based on an elementary yet versatile non-asymptotic approach.
  arXiv  Detail & Related papers  (2023-06-15T16:30:08Z)
• Precision-Recall Divergence Optimization for Generative Modeling with GANs and Normalizing Flows [54.050498411883495]
  We develop a novel training method for generative models, such as Generative Adversarial Networks and Normalizing Flows. We show that achieving a specified precision-recall trade-off corresponds to minimizing a unique $f$-divergence from a family we call the textitPR-divergences. Our approach improves the performance of existing state-of-the-art models like BigGAN in terms of either precision or recall when tested on datasets such as ImageNet.
  arXiv  Detail & Related papers  (2023-05-30T10:07:17Z)
• Equivariant Discrete Normalizing Flows [10.867162810786361]
  We focus on building equivariant normalizing flows using discrete layers. We introduce two new equivariant flows: $G$-coupling Flows and $G$-Residual Flows. Our construction of $G$-Residual Flows are also universal, in the sense that we prove an $G$-equivariant diffeomorphism can be exactly mapped by a $G$-residual flow.
  arXiv  Detail & Related papers  (2021-10-16T20:16:00Z)
• Gaussianization Flows [113.79542218282282]
  We propose a new type of normalizing flow model that enables both efficient iteration of likelihoods and efficient inversion for sample generation. Because of this guaranteed expressivity, they can capture multimodal target distributions without compromising the efficiency of sample generation.
  arXiv  Detail & Related papers  (2020-03-04T08:15:06Z)

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.