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Fisher Score

In statistics, the gradient of the log-likelihood with respect to the model parameters, a fundamental concept underlying score matching for parametric estimation.

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Sliced Score Matching

A variant of score matching that reduces computational complexity by projecting the gradient onto random directions, making training more efficient for high-dimensional data.

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Poisson Equation

Partial differential equation linking the vector field of the score to the Laplacian of the logarithm of the density, whose resolution is central in score-based methods.

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Stochastic Langevin

Diffusion process or sampling algorithm that uses the gradient of the log-density (the score) to guide sampling towards high-probability regions.

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Score Vector Field

Spatial representation of the score at each point in the data space, indicating the direction and magnitude of the strongest increase in probability density.

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Stein Divergence

Dissimilarity metric between distributions based on Stein test functions, closely related to the score matching objective and used to evaluate the quality of the score model.

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Denoising Paradox

Phenomenon where training a score model on noisy data (denoising) yields better results for estimating the score of clean data than direct training.

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Score-Based Generative Modeling

Generative modeling paradigm where a neural network is trained to estimate the score of the data distribution at multiple noise levels, then used for generation via a reverse diffusion process.

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Score Multiplicity

Concept where a single score model can be used to generate samples from different distributions by changing the noise level or initial condition of the diffusion process.

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Fokker-Planck Equation

Partial differential equation describing the time evolution of the probability density of a stochastic process, fundamental for understanding the theory behind diffusion and score models.

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Score Bias Correction

Technique aimed at adjusting score predictions to compensate for biases introduced by model approximation or the use of noisy data, essential for accurate estimation.

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Score-Based Normalizing Flow

Hybrid approach where score information is used to design or improve transformations in a normalizing flow model, combining the advantages of both paradigms.

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Score Matching Criterion

Objective function, often a form of distance between the predicted score and the true score, that is minimized during training to learn an accurate score model.

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Score Interpolation

Process of estimating the score for intermediate noise levels by interpolating model predictions, used in multi-scale diffusion models.

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Conditional Score

Extension of score matching where the learned score is conditioned on metadata (e.g., class labels), allowing directional control over the generation process.

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