Score Function
The gradient of the log-density of a data distribution, ∇_x log p(x). It is central to the denoising process in diffusion models and is approximated in practice by a neural network (score network) trained to minimize the mean squared error between predicted and true scores.
Core Facts
Timeline (last 90 days)
The target score identity expresses the score function as a self-consistent relation between the current model prediction and the gradient of the unnormalized density, making it possible to construct a training objective without external training data.
The score function learned in S³-PnP is used to correct the input of the analytic prior update, combining the observation-driven correction term with analytic regularization, so that the prior emerges naturally from the current observation and the ADMM iteration process rather than being borrowed externally.
Diffusion models achieve generation and denoising by training a network to approximate the score function ∇_x log p_σ(x) at each noise level.
The Hyvärinen score is defined as the gradient of the log density with respect to the input, ∇_x log p(x), and does not depend on the normalization constant.
All Facts (5)
The core driving force of the reverse process in diffusion models is the Score function, i.e., the log-density gradient ∇x log p(x), which points in the direction of the steepest increase in probability density.
75%UnverifiedThe target score identity expresses the score function as a self-consistent relation between the current model prediction and the gradient of the unnormalized density, making it possible to construct a training objective without external training data.
50%UnverifiedThe score function learned in S³-PnP is used to correct the input of the analytic prior update, combining the observation-driven correction term with analytic regularization, so that the prior emerges naturally from the current observation and the ADMM iteration process rather than being borrowed externally.
50%UnverifiedDiffusion models achieve generation and denoising by training a network to approximate the score function ∇_x log p_σ(x) at each noise level.
50%UnverifiedThe Hyvärinen score is defined as the gradient of the log density with respect to the input, ∇_x log p(x), and does not depend on the normalization constant.
50%