Related papers: On the exact relationship between the denoising fu…

Confirmation bias, the tendency to interpret information in a way that aligns with one's preconceptions, can profoundly impact scientific research, leading to conclusions that reflect the researcher's hypotheses even when the observational…

Today's denoising diffusion models do not "denoise" in the classical sense, i.e., they do not directly predict clean images. Rather, the neural networks predict noise or a noised quantity. In this paper, we suggest that predicting clean…

We study the problem of super-resolution, where we recover the locations and weights of non-negative point sources from a few samples of their convolution with a Gaussian kernel. It has been shown that exact recovery is possible by…

Compared with traditional seismic noise attenuation algorithms that depend on signal models and their corresponding prior assumptions, removing noise with a deep neural network is trained based on a large training set, where the inputs are…

Face anti-spoofing is crucial for ensuring the security and reliability of face recognition systems. Several existing face anti-spoofing methods utilize GAN-like networks to detect presentation attacks by estimating the noise pattern of a…

We consider the additive white Gaussian noise channels. We prove that the error probability of decoding tends to one exponentially for rates above the capacity and derive the optimal exponent function. We shall demonstrate that the…

Whilst deep neural networks have shown great empirical success, there is still much work to be done to understand their theoretical properties. In this paper, we study the relationship between random, wide, fully connected, feedforward…

It has been generally recognized that stochasticity can play an important role in the information processing accomplished by reaction networks in biological cells. Most treatments of that stochasticity employ Gaussian noise even though it…

Sensor placement approaches in networks often involve using information-theoretic measures such as entropy and mutual information. We prove that mutual information abides by submodularity and is non-decreasing when considering the mutual…

Recent years have witnessed significant progress in developing effective training and fast sampling techniques for diffusion models. A remarkable advancement is the use of stochastic differential equations (SDEs) and their…

We consider the problem of mean estimation assuming only finite variance. We study a new class of mean estimators constructed by integrating over random noise applied to a soft-truncated empirical mean estimator. For appropriate choices of…

Diffusion and flow-based generative models have shown strong potential for image restoration. However, image denoising under unknown and varying noise conditions remains challenging, because the learned vector fields may become inconsistent…

Image denoising and high-level vision tasks are usually handled independently in the conventional practice of computer vision, and their connection is fragile. In this paper, we cope with the two jointly and explore the mutual influence…

Recent work has shown that Transformers can perform in-context learning for linear regression under restrictive assumptions, including i.i.d. data, Gaussian noise, and Gaussian regression coefficients. However, real-world data often violate…

Recently, Generative Adversarial Networks (GANs) have emerged as a popular alternative for modeling complex high dimensional distributions. Most of the existing works implicitly assume that the clean samples from the target distribution are…

Diffusion models generalize well in practice. However, an optimal diffusion model fully memorizes the training data and therefore fails to generalize, raising the question of what induces generalization in a real diffusion model. We show…

The interdependence and high dimensionality of multivariate signals present significant challenges for denoising, as conventional univariate methods often struggle to capture the complex interactions between variables. A successful approach…

A major challenge in understanding the generalization of deep learning is to explain why (stochastic) gradient descent can exploit the network architecture to find solutions that have good generalization performance when using high capacity…

Motivated by distributed machine learning settings such as Federated Learning, we consider the problem of fitting a statistical model across a distributed collection of heterogeneous data sets whose similarity structure is encoded by a…

Recently, research on denoising diffusion models has expanded its application to the field of image restoration. Traditional diffusion-based image restoration methods utilize degraded images as conditional input to effectively guide the…