Generative Neural Operators through Diffusion Last Layer

• URL: http://arxiv.org/abs/2602.04139v1
• Date: Wed, 04 Feb 2026 02:10:53 GMT
• Title: Generative Neural Operators through Diffusion Last Layer
• Authors: Sungwon Park, Anthony Zhou, Hongjoong Kim, Amir Barati Farimani,
• Abstract summary: We introduce a lightweight probabilistic head that can be attached to arbitrary neural operator backbones to model predictive uncertainty.<n>Motivated by the relative smoothness and low-dimensional structure often exhibited by PDE solution distributions, we parameterize the conditional output distribution directly in function space.<n>Across PDE operator learning benchmarks, prediction improves and uncertainty-aware.
• Score: 13.076028397183897
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Neural operators have emerged as a powerful paradigm for learning discretization-invariant function-to-function mappings in scientific computing. However, many practical systems are inherently stochastic, making principled uncertainty quantification essential for reliable deployment. To address this, we introduce a simple add-on, the diffusion last layer (DLL), a lightweight probabilistic head that can be attached to arbitrary neural operator backbones to model predictive uncertainty. Motivated by the relative smoothness and low-dimensional structure often exhibited by PDE solution distributions, DLL parameterizes the conditional output distribution directly in function space through a low-rank Karhunen-Loève expansion, enabling efficient and expressive uncertainty modeling. Across stochastic PDE operator learning benchmarks, DLL improves generalization and uncertainty-aware prediction. Moreover, even in deterministic long-horizon rollout settings, DLL enhances rollout stability and provides meaningful estimates of epistemic uncertainty for backbone neural operators.

Related papers

• GTS: Inference-Time Scaling of Latent Reasoning with a Learnable Gaussian Thought Sampler [54.10960908347221]
  We model latent thought exploration as conditional sampling from learnable densities and instantiate this idea as a Gaussian Thought Sampler (GTS)<n>GTS predicts context-dependent perturbation distributions over continuous reasoning states and is trained with GRPO-style policy optimization while keeping the backbone frozen.
  arXiv  Detail & Related papers  (2026-02-15T09:57:47Z)
• KoopGen: Koopman Generator Networks for Representing and Predicting Dynamical Systems with Continuous Spectra [65.11254608352982]
  We introduce a generator-based neural Koopman framework that models dynamics through a structured, state-dependent representation of Koopman generators.<n>By exploiting the intrinsic Cartesian decomposition into skew-adjoint and self-adjoint components, KoopGen separates conservative transport from irreversible dissipation.
  arXiv  Detail & Related papers  (2026-02-15T06:32:23Z)
• Kantorovich-Type Stochastic Neural Network Operators for the Mean-Square Approximation of Certain Second-Order Stochastic Processes [0.0]
  We construct a new class of textbfKantorovich-type Neural Network Operators (K-SNNOs) in which randomness is incorporated not at the coefficient level, but through textbfstochastic neurons driven by neurons.<n>This framework enables the operator to inherit the probabilistic structure of the underlying process, making it suitable for modeling and approximating signals.
  arXiv  Detail & Related papers  (2026-01-07T06:25:40Z)
• Light-Weight Diffusion Multiplier and Uncertainty Quantification for Fourier Neural Operators [1.315766151337659]
  We introduce DINOZAUR: a diffusion-based neural operator parametrization with uncertainty quantification.<n>Our method achieves competitive or superior performance across several PDE benchmarks.
  arXiv  Detail & Related papers  (2025-08-01T13:57:19Z)
• LVM-GP: Uncertainty-Aware PDE Solver via coupling latent variable model and Gaussian process [9.576396359649921]
  We propose a novel framework, termed LVM-GP, for uncertainty quantification in solving PDEs with noisy data.<n>The architecture consists of a confidence-aware encoder and a probabilistic decoder.
  arXiv  Detail & Related papers  (2025-07-30T09:00:39Z)
• A Simple Approximate Bayesian Inference Neural Surrogate for Stochastic Petri Net Models [0.0]
  We introduce a neural-network-based approximation of the posterior distribution framework.<n>Our model employs a lightweight 1D Convolutional Residual Network trained end-to-end on Gillespie-simulated SPN realizations.<n>On synthetic SPNs with 20% missing events, our surrogate recovers rate-function coefficients with an RMSE = 0.108 and substantially runs faster than traditional Bayesian approaches.
  arXiv  Detail & Related papers  (2025-07-14T18:31:19Z)
• Efficient Parametric SVD of Koopman Operator for Stochastic Dynamical Systems [51.54065545849027]
  The Koopman operator provides a principled framework for analyzing nonlinear dynamical systems.<n>VAMPnet and DPNet have been proposed to learn the leading singular subspaces of the Koopman operator.<n>We propose a scalable and conceptually simple method for learning the top-$k$ singular functions of the Koopman operator.
  arXiv  Detail & Related papers  (2025-07-09T18:55:48Z)
• Elucidated Rolling Diffusion Models for Probabilistic Weather Forecasting [52.6508222408558]
  We introduce Elucidated Rolling Diffusion Models (ERDM)<n>ERDM is the first framework to unify a rolling forecast structure with the principled, performant design of Elucidated Diffusion Models (EDM)<n>On 2D Navier-Stokes simulations and ERA5 global weather forecasting at 1.5circ resolution, ERDM consistently outperforms key diffusion-based baselines.
  arXiv  Detail & Related papers  (2025-06-24T21:44:31Z)
• Latent Diffusion Model Based Denoising Receiver for 6G Semantic Communication: From Stochastic Differential Theory to Application [11.385703484113552]
  We propose a novel semantic communication framework empowered by generative artificial intelligence (GAI)<n>A latent diffusion model (LDM)-based semantic communication framework is proposed that combines a variational autoencoder for semantic features extraction.<n>The proposed system is a training-free framework that supports zero-shot generalization, and achieves superior performance under low-SNR and out-of-distribution conditions.
  arXiv  Detail & Related papers  (2025-06-06T03:20:32Z)
• Probabilistic neural operators for functional uncertainty quantification [14.08907045605149]
  We introduce the probabilistic neural operator (PNO), a framework for learning probability distributions over the output function space of neural operators.<n>PNO extends neural operators with generative modeling based on strictly proper scoring rules, integrating uncertainty information directly into the training process.
  arXiv  Detail & Related papers  (2025-02-18T14:42:11Z)
• Tractable Function-Space Variational Inference in Bayesian Neural Networks [72.97620734290139]
  A popular approach for estimating the predictive uncertainty of neural networks is to define a prior distribution over the network parameters. We propose a scalable function-space variational inference method that allows incorporating prior information. We show that the proposed method leads to state-of-the-art uncertainty estimation and predictive performance on a range of prediction tasks.
  arXiv  Detail & Related papers  (2023-12-28T18:33:26Z)
• Monte Carlo Neural PDE Solver for Learning PDEs via Probabilistic Representation [59.45669299295436]
  We propose a Monte Carlo PDE solver for training unsupervised neural solvers.<n>We use the PDEs' probabilistic representation, which regards macroscopic phenomena as ensembles of random particles.<n>Our experiments on convection-diffusion, Allen-Cahn, and Navier-Stokes equations demonstrate significant improvements in accuracy and efficiency.
  arXiv  Detail & Related papers  (2023-02-10T08:05:19Z)
• Which Invariance Should We Transfer? A Causal Minimax Learning Approach [18.71316951734806]
  We present a comprehensive minimax analysis from a causal perspective. We propose an efficient algorithm to search for the subset with minimal worst-case risk. The effectiveness and efficiency of our methods are demonstrated on synthetic data and the diagnosis of Alzheimer's disease.
  arXiv  Detail & Related papers  (2021-07-05T09:07:29Z)
• Multiplicative noise and heavy tails in stochastic optimization [62.993432503309485]
  empirical optimization is central to modern machine learning, but its role in its success is still unclear. We show that it commonly arises in parameters of discrete multiplicative noise due to variance. A detailed analysis is conducted in which we describe on key factors, including recent step size, and data, all exhibit similar results on state-of-the-art neural network models.
  arXiv  Detail & Related papers  (2020-06-11T09:58:01Z)

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.