Related papers: Nonlinear denoising score matching for enhanced le…

Reconstructing noise-driven nonlinear networks from time series of output variables is a challenging problem, which turns to be very difficult when nonlinearity of dynamics, strong noise impacts and low measurement frequencies jointly…

To fully understand, analyze, and determine the behavior of dynamical systems, it is crucial to identify their intrinsic modal coordinates. In nonlinear dynamical systems, this task is challenging as the modal transformation based on the…

Consistency models possess high capabilities for image generation, advancing sampling steps to a single step through their advanced techniques. Current advancements move one step forward consistency training techniques and eliminates the…

Energy-Based Models (EBMs) offer a versatile framework for modeling complex data distributions. However, training and sampling from EBMs continue to pose significant challenges. The widely-used Denoising Score Matching (DSM) method for…

Conventional research attributes the improvements of generalization ability of deep neural networks either to powerful optimizers or the new network design. Different from them, in this paper, we aim to link the generalization ability of a…

Score-based generative modeling (SBGM) has achieved state-of-the-art performance in image generation, with the quality of generated images being highly dependent on the design of the forward (diffusion) process. Among these, models based on…

This paper demonstrates how to recover causal graphs from the score of the data distribution in non-linear additive (Gaussian) noise models. Using score matching algorithms as a building block, we show how to design a new generation of…

Denoising diffusion models have emerged as the go-to generative framework for solving inverse problems in imaging. A critical concern regarding these models is their performance on out-of-distribution tasks, which remains an under-explored…

Several machine learning applications involve the optimization of higher-order derivatives (e.g., gradients of gradients) during training, which can be expensive in respect to memory and computation even with automatic differentiation. As a…

We propose a novel method of introducing structure into existing machine learning techniques by developing structure-based similarity and distance measures. To learn structural information, low-dimensional structure of the data is captured…

We introduce a constructive framework to learn effective Langevin equations from stationary time series. Unlike conventional approaches that require iterative calibration to match target statistics, our construction guarantees the observed…

Denoising score matching plays a pivotal role in the performance of diffusion-based generative models. However, the empirical optimal score--the exact solution to the denoising score matching--leads to memorization, where generated samples…

In the field of inverse estimation for systems modeled by partial differential equations (PDEs), challenges arise when estimating high- (or even infinite-) dimensional parameters. Typically, the ill-posed nature of such problems…

We introduce a new adaptive decomposition tool, which we refer to as Nonlinear Mode Decomposition (NMD). It decomposes a given signal into a set of physically meaningful oscillations for any waveform, simultaneously removing the noise. NMD…

Diffusion models have recently emerged as a powerful framework for generative modeling. They consist of a forward process that perturbs input data with Gaussian white noise and a reverse process that learns a score function to generate…

We study the training objectives of denoising-based generative models, with a particular focus on loss weighting and output parameterization, including noise-, clean image-, and velocity-based formulations. Through a systematic numerical…

Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…

In this paper, we design a novel distributed learning algorithm using stochastic compressed communications. In detail, we pursue a modular approach, merging ADMM and a gradient-based approach, benefiting from the robustness of the former…

Score-based models generate samples by mapping noise to data (and vice versa) via a high-dimensional diffusion process. We question whether it is necessary to run this entire process at high dimensionality and incur all the inconveniences…

We consider the problem of denoising with the help of prior information taken from a database of clean signals or images. Denoising with variational methods is very efficient if a regularizer well adapted to the nature of the data is…