Related papers: Sliced Score Matching: A Scalable Approach to Dens…

Estimating means on Riemannian manifolds is generally computationally expensive because the Riemannian distance function is not known in closed-form for most manifolds. To overcome this, we show that Riemannian diffusion means can be…

By learning the gradient of smoothed data distributions, diffusion models can iteratively generate samples from complex distributions. The learned score function enables their generalization capabilities, but how the learned score relates…

In this work, we investigated the application of score-based gradient learning in discriminative and generative classification settings. Score function can be used to characterize data distribution as an alternative to density. It can be…

We investigate the approximation efficiency of score functions by deep neural networks in diffusion-based generative modeling. While existing approximation theories utilize the smoothness of score functions, they suffer from the curse of…

Score diffusion methods can learn probability densities from samples. The score of the noise-corrupted density is estimated using a deep neural network, which is then used to iteratively transport a Gaussian white noise density to a target…

Many existing conditional score-based data generation methods utilize Bayes' theorem to decompose the gradients of a log posterior density into a mixture of scores. These methods facilitate the training procedure of conditional score…

Seeking informative projecting directions has been an important task in utilizing sliced Wasserstein distance in applications. However, finding these directions usually requires an iterative optimization procedure over the space of…

We present a novel method for training score-based generative models which uses nonlinear noising dynamics to improve learning of structured distributions. Generalizing to a nonlinear drift allows for additional structure to be incorporated…

Conditional density estimation is a general framework for solving various problems in machine learning. Among existing methods, non-parametric and/or kernel-based methods are often difficult to use on large datasets, while methods based on…

Distribution matching (DM) is a versatile domain-invariant representation learning technique that has been applied to tasks such as fair classification, domain adaptation, and domain translation. Non-parametric DM methods struggle with…

Diffusion models are widely used in applications ranging from image generation to inverse problems. However, training diffusion models typically requires clean ground-truth images, which are unavailable in many applications. We introduce…

Reversing a diffusion process by learning its score forms the heart of diffusion-based generative modeling and for estimating properties of scientific systems. The diffusion processes that are tractable center on linear processes with a…

The density estimation is one of the core problems in statistics. Despite this, existing techniques like maximum likelihood estimation are computationally inefficient due to the intractability of the normalizing constant. For this reason an…

Compositional data and multivariate count data with known totals are challenging to analyse due to the non-negativity and sum-to-one constraints on the sample space. It is often the case that many of the compositional components are highly…

Score Distillation Sampling (SDS) is a recent but already widely popular method that relies on an image diffusion model to control optimization problems using text prompts. In this paper, we conduct an in-depth analysis of the SDS loss…

It has previously been shown that ordinary least squares can be used to estimate the coefficients of the single-index model under only mild conditions. However, the estimator is non-robust leading to poor estimates for some models. In this…

Denoising score matching (DSM) for training diffusion models may suffer from high variance at low noise levels. Target Score Matching (TSM) mitigates this when clean data scores are available, providing a low-variance objective. In many…

One of the major problems for maximum likelihood estimation in the well-established directional models is that the normalising constants can be difficult to evaluate. A new general method of "score matching estimation" is presented here on…

Noise contrastive estimation (NCE) is a popular method for training energy-based models (EBM) with intractable normalisation terms. The key idea of NCE is to learn by comparing unnormalised log-likelihoods of the reference and noisy…

The efficient evaluation of high-dimensional integrals is of importance in both theoretical and practical fields of science, such as data science, statistical physics, and machine learning. However, exact computation methods suffer from the…