Understanding Diffusion Models via Ratio-Based Function Approximation with SignReLU Networks

• URL: http://arxiv.org/abs/2601.21242v1
• Date: Thu, 29 Jan 2026 04:01:54 GMT
• Title: Understanding Diffusion Models via Ratio-Based Function Approximation with SignReLU Networks
• Authors: Luwei Sun, Dongrui Shen, Jianfe Li, Yulong Zhao, Han Feng,
• Abstract summary: Motivated by challenges in conditional generative modeling, this paper develops a theoretical framework for approximating such ratio-type functionals.<n>We provide a concise proof for approximating these ratio-type functionals using deep neural networks with the SignReLU activation function.
• Score: 3.6895681517492407
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Motivated by challenges in conditional generative modeling, where the target conditional density takes the form of a ratio f1 over f2, this paper develops a theoretical framework for approximating such ratio-type functionals. Here, f1 and f2 are kernel-based marginal densities that capture structured interactions, a setting central to diffusion-based generative models. We provide a concise proof for approximating these ratio-type functionals using deep neural networks with the SignReLU activation function, leveraging the activation's piecewise structure. Under standard regularity assumptions, we establish L^p(Omega) approximation bounds and convergence rates. Specializing to Denoising Diffusion Probabilistic Models (DDPMs), we construct a SignReLU-based neural estimator for the reverse process and derive bounds on the excess Kullback-Leibler (KL) risk between the generated and true data distributions. Our analysis decomposes this excess risk into approximation and estimation error components. These results provide generalization guarantees for finite-sample training of diffusion-based generative models.

Related papers

• FlexCausal: Flexible Causal Disentanglement via Structural Flow Priors and Manifold-Aware Interventions [1.7114074082429929]
  Causal Disentangled Representation Learning aims to learn and disentangle low dimensional representations from observations.<n>We propose FlexCausal, a novel CDRL framework based on a block-diagonal covariance VAE.<n>Our framework ensures a precise structural correspondence between the learned latent subspaces and the ground-truth causal relations.
  arXiv  Detail & Related papers  (2026-01-29T11:30:53Z)
• Non-asymptotic error bounds for probability flow ODEs under weak log-concavity [6.661419982187023]
  This work establishes non-asymptotic convergence bounds in the 2-Wasserstein distance for a general class of probability flow ODEs.<n>Our results extend convergence theory to more realistic data distributions and practical ODE solvers.
  arXiv  Detail & Related papers  (2025-10-20T14:54:38Z)
• Non-asymptotic convergence bound of conditional diffusion models [2.0410061496886454]
  We develop a conditional diffusion model within the domains of classification and regression.<n>It integrates a pre-trained model f_phi(x) into the original diffusion model framework.<n>When f_phi(x) performs satisfactorily, Y|fphi(x) closely approximates Y|X.
  arXiv  Detail & Related papers  (2025-08-13T13:35:56Z)
• Score-Based Model for Low-Rank Tensor Recovery [49.158601255093416]
  Low-rank tensor decompositions (TDs) provide an effective framework for multiway data analysis.<n>Traditional TD methods rely on predefined structural assumptions, such as CP or Tucker decompositions.<n>We propose a score-based model that eliminates the need for predefined structural or distributional assumptions.
  arXiv  Detail & Related papers  (2025-06-27T15:05:37Z)
• Overcoming Dimensional Factorization Limits in Discrete Diffusion Models through Quantum Joint Distribution Learning [79.65014491424151]
  We propose a quantum Discrete Denoising Diffusion Probabilistic Model (QD3PM)<n>It enables joint probability learning through diffusion and denoising in exponentially large Hilbert spaces.<n>This paper establishes a new theoretical paradigm in generative models by leveraging the quantum advantage in joint distribution learning.
  arXiv  Detail & Related papers  (2025-05-08T11:48:21Z)
• Rectified Diffusion Guidance for Conditional Generation [94.83538269086613]
  We revisit the theory behind CFG and rigorously confirm that the improper combination coefficients (textiti.e.) brings about expectation shift the generative distribution.<n>We show that our approach enjoys a textbftextitform solution given the strength.<n> Empirical evidence on real-world data demonstrate the compatibility of our design with existing state-of-the-art diffusion models.
  arXiv  Detail & Related papers  (2024-10-24T13:41:32Z)
• Wasserstein proximal operators describe score-based generative models and resolve memorization [12.321631823103894]
  We first formulate SGMs in terms of the Wasserstein proximal operator (WPO) We show that WPO describes the inductive bias of diffusion and score-based models. We present an interpretable kernel-based model for the score function which dramatically improves the performance of SGMs.
  arXiv  Detail & Related papers  (2024-02-09T03:33:13Z)
• Analyzing Neural Network-Based Generative Diffusion Models through Convex Optimization [45.72323731094864]
  We present a theoretical framework to analyze two-layer neural network-based diffusion models. We prove that training shallow neural networks for score prediction can be done by solving a single convex program. Our results provide a precise characterization of what neural network-based diffusion models learn in non-asymptotic settings.
  arXiv  Detail & Related papers  (2024-02-03T00:20:25Z)
• Reflected Diffusion Models [93.26107023470979]
  We present Reflected Diffusion Models, which reverse a reflected differential equation evolving on the support of the data. Our approach learns the score function through a generalized score matching loss and extends key components of standard diffusion models.
  arXiv  Detail & Related papers  (2023-04-10T17:54:38Z)
• Diffusion Models are Minimax Optimal Distribution Estimators [49.47503258639454]
  We provide the first rigorous analysis on approximation and generalization abilities of diffusion modeling. We show that when the true density function belongs to the Besov space and the empirical score matching loss is properly minimized, the generated data distribution achieves the nearly minimax optimal estimation rates.
  arXiv  Detail & Related papers  (2023-03-03T11:31:55Z)
• Diffusion Causal Models for Counterfactual Estimation [18.438307666925425]
  We consider the task of counterfactual estimation from observational imaging data given a known causal structure. We propose Diff-SCM, a deep structural causal model that builds on recent advances of generative energy-based models. We find that Diff-SCM produces more realistic and minimal counterfactuals than baselines on MNIST data and can also be applied to ImageNet data.
  arXiv  Detail & Related papers  (2022-02-21T12:23:01Z)
• Learning Likelihoods with Conditional Normalizing Flows [54.60456010771409]
  Conditional normalizing flows (CNFs) are efficient in sampling and inference. We present a study of CNFs where the base density to output space mapping is conditioned on an input x, to model conditional densities p(y|x)
  arXiv  Detail & Related papers  (2019-11-29T19:17:58Z)

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.