Score Function
The gradient of the log-density of a data distribution with respect to the sample, denoted ∇_x log p(x). It is a central concept in score-based generative models such as diffusion models, and was systematically introduced by Hyvärinen (2005) within the score matching framework. It points in the direction of steepest ascent of the data density.
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The Stein identity states that for a function φ that decays sufficiently fast on the boundary, when the probability density p(x) is sufficiently smooth on R^d, E_p[∇_x log p(x)·φ(x) + ∇_x·φ(x)] = 0.
In diffusion models, the score function is used to describe the log gradient of the data distribution and is trained via denoising score matching.
The score function ∇_x log p(x) was systematically introduced by Hyvärinen in 2005 within the score matching framework
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The Stein identity states that for a function φ that decays sufficiently fast on the boundary, when the probability density p(x) is sufficiently smooth on R^d, E_p[∇_x log p(x)·φ(x) + ∇_x·φ(x)] = 0.
50%UnverifiedIn diffusion models, the score function is used to describe the log gradient of the data distribution and is trained via denoising score matching.
50%UnverifiedThe score function ∇_x log p(x) was systematically introduced by Hyvärinen in 2005 within the score matching framework
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