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Stochastic Transformation

Mathematical process applying progressive random transformations to data, enabling controlled transition between probability distributions in latent space.

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Score-Based Model

Neural network architecture learning to predict the gradient of the log-probability potential field, used to reverse stochastic diffusion processes.

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Reverse Diffusion Process

Regressive phase learning to iteratively denoise data, reconstructing the original sample from noise using estimated score gradients.

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Fokker-Planck Equation

Partial differential equation describing the temporal evolution of probability density in diffusion processes, directly linking SDE to distributional dynamics.

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Ornstein-Uhlenbeck Process

Stationary stochastic process with mean reversion, fundamentally used in diffusion models to control the dynamics of noise addition and removal.

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Diffusion Rate

Scalar parameter controlling the intensity of noise added at each time step, determining the speed and stability of stochastic transformation.

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Continuous Markov Chain

Continuous-time stochastic process where future states depend only on the present state, providing the mathematical foundation for differential diffusion models.

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Score Function

Gradient of the logarithm of probability density with respect to data, pointing toward high-density regions and guiding noise deconstruction in generative models.

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Continuous Diffusion Time

Normalized positive real parameter in [0,1] representing the continuous evolution of the stochastic process, enabling a unified differential formulation.

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Estimated Score Gradients

Numerical approximations of log-likelihood gradients computed by neural networks, replacing inaccessible analytical gradients in complex distributions.

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