Related papers: Technical Note on Relating Scores of Tilted Distri…
We examine theoretical properties of the denoising score matching estimate. We model the density of observations with a nonparametric Gaussian mixture. We significantly relax the standard manifold assumption allowing the samples step away…
Diffusion models are gaining widespread use in cutting-edge image, video, and audio generation. Score-based diffusion models stand out among these methods, necessitating the estimation of score function of the input data distribution. In…
We consider random walk on a mildly random environment on finite transitive d- regular graphs of increasing girth. After scaling and centering, the analytic spectrum of the transition matrix converges in distribution to a Gaussian noise. An…
The score test statistic using the observed information is easy to compute numerically. Its large sample distribution under the null hypothesis is well known and is equivalent to that of the score test based on the expected information, the…
In this paper we consider a random variable $Y$ contamined by an independent additive noise $Z$. We assume that $Z$ has known distribution. Our purpose is to test the distribution of the unobserved random variable $Y$. We propose a data…
Density regression characterizes the conditional density of the response variable given the covariates, and provides much more information than the commonly used conditional mean or quantile regression. However, it is often computationally…
We present analytical expressions for the time-dependent and stationary probability distributions corresponding to a stochastically perturbed one-dimensional flow with critical points, in two physically relevant situations: delayed…
The 't Hooft criterion leading to confinement out of a percolating cluster of central vortices suggests defining a novel three-dimensional gauge theory directly on a random percolation process. Wilson loop is viewed as a counter of…
Relative Fisher information, also known as score matching, is a recently introduced learning method for parameter estimation. Fundamental relations between relative entropy and score matching have been established in the literature for…
I calculate the noise in the measured correlation functions and spectra of digitized, noiselike signals. In the spectral domain, the signals are drawn from a Gaussian distribution with variance that depends on frequency. Nearly all…
Diffusion models are loosely modelled based on non-equilibrium thermodynamics, where \textit{diffusion} refers to particles flowing from high-concentration regions towards low-concentration regions. In statistics, the meaning is quite…
If a probability density p(\x) (\x\in\R^k) is bounded and R(t) := \int \exp(t\ell(\x)) \d\x < \infty for some linear functional \ell and all t\in(0,1), then, for each t\in(0,1) and all large enough n, the n-fold convolution of the t-tilted…
We study the problem of training diffusion and flow generative models to sample from target distributions defined by an exponential tilting of a base density; a formulation that subsumes both sampling from unnormalized densities and reward…
Score matching is a recently developed parameter learning method that is particularly effective to complicated high dimensional density models with intractable partition functions. In this paper, we study two issues that have not been…
Representing probability distributions by the gradient of their density functions has proven effective in modeling a wide range of continuous data modalities. However, this representation is not applicable in discrete domains where the…
Diffuse two-dimensional integer-valued arrays are demonstrated that have delta-like aperiodic autocorrelation and, simultaneously, the array sums form delta-like projections along several directions. The delta-projected views show a single…
Score-based diffusion models have demonstrated outstanding empirical performance in machine learning and artificial intelligence, particularly in generating high-quality new samples from complex probability distributions. Improving the…
We present a mechanism to steer the sampling diversity of denoising diffusion and flow matching models, allowing users to sample from a sharper or broader distribution than the training distribution. We build on the observation that these…
We experimentally test the effects of tilting a turbulent Rayleigh-B{\'e}nard convection cell on the dynamics of the large-scale circulation (LSC) orientation $\theta_0$. The probability distribution of $\theta_0$ is measured, and used to…
The Voigt profile is the density obtained from the convolution of a Gaussian and a Cauchy and it is widely used in atomic and molecular spectroscopy. We show that the Voigt profile is a scale mixture of Gaussian distributions, with mixing…