Related papers: Heavy-tailed denoising score matching
Flow matching has emerged as a powerful generative modeling approach with flexible choices of source distribution. While Gaussian distributions are commonly used, the potential for better alternatives in high-dimensional data generation…
Denoising has always been theoretically considered as removal of high frequency disturbances having Gaussian distribution. Here we relax this assumption and the method used here is completely different from traditional thresholding schemes.…
To improve the off-sample generalization of classical procedures minimizing the empirical risk under potentially heavy-tailed data, new robust learning algorithms have been proposed in recent years, with generalized median-of-means…
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…
We address the problem of image denoising in additive white noise without placing restrictive assumptions on its statistical distribution. In the recent literature, specific noise distributions have been considered and correspondingly,…
It is not uncommon that real-world data are distributed with a long tail. For such data, the learning of deep neural networks becomes challenging because it is hard to classify tail classes correctly. In the literature, several existing…
Score-based diffusion models, which generate new data by learning to reverse a diffusion process that perturbs data from the target distribution into noise, have achieved remarkable success across various generative tasks. Despite their…
This work introduces a sampling method capable of solving Bayesian inverse problems in function space. It does not assume the log-concavity of the likelihood, meaning that it is compatible with nonlinear inverse problems. The method…
A novel statistical method is proposed and investigated for estimating a heavy tailed density under mild smoothness assumptions. Statistical analyses of heavy-tailed distributions are susceptible to the problem of sparse information in the…
Gravitational wave detectors will need optimal signal-processing algorithms to extract weak signals from the detector noise. Most algorithms designed to date are based on the unrealistic assumption that the detector noise may be modeled as…
Score-based generative models can effectively learn the distribution of data by estimating the gradient of the distribution. Due to the multi-step denoising characteristic, researchers have recently considered combining score-based…
We study convergence in high-probability of SGD-type methods in non-convex optimization and the presence of heavy-tailed noise. To combat the heavy-tailed noise, a general black-box nonlinear framework is considered, subsuming…
Denoising diffusion models have proven to be a flexible and effective paradigm for generative modelling. Their recent extension to infinite dimensional Euclidean spaces has allowed for the modelling of stochastic processes. However, many…
Diffusion models typically inject isotropic Gaussian noise, disregarding structure in the data. Motivated by the way quantum squeezed states redistribute uncertainty according to the Heisenberg uncertainty principle, we introduce Squeezed…
Solving ill-posed inverse problems requires careful formulation of prior beliefs over the signals of interest and an accurate description of their manifestation into noisy measurements. Handcrafted signal priors based on e.g. sparsity are…
Although stochastic optimization is central to modern machine learning, the precise mechanisms underlying its success, and in particular, the precise role of the stochasticity, still remain unclear. Modelling stochastic optimization…
Seismic data denoising is an important part of seismic data processing, which directly relate to the follow-up processing of seismic data. In terms of this issue, many authors proposed many methods based on rank reduction, sparse…
We prove an exact relationship between the optimal denoising function and the data distribution in the case of additive Gaussian noise, showing that denoising implicitly models the structure of data allowing it to be exploited in the…
Many parametric statistical models are not properly normalised and only specified up to an intractable partition function, which renders parameter estimation difficult. Examples of unnormalised models are Gibbs distributions, Markov random…
Multi-modal hashing methods have gained popularity due to their fast speed and low storage requirements. Among them, the supervised methods demonstrate better performance by utilizing labels as supervisory signals compared with unsupervised…