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Stochastic Diffusion
Generation process where each denoising step incorporates a random component, allowing exploration of the solution space and generating varied samples from the same noisy input.
Deterministic Diffusion
Denoising approach where the reverse process follows a unique and predictable trajectory, often modeled as an ODE solver, eliminating all stochasticity to produce a reproducible result.
ODE Solver
Numerical method used to solve the ordinary differential equations governing the deterministic diffusion process, ensuring a unique and stable denoising trajectory.
Langevin Sampler
Stochastic MCMC-type algorithm that uses the gradient of the log probability density to perform a random walk, serving as the basis for the denoising process in stochastic diffusion models.
Additive Gaussian Noise
Noising process where noise following a normal distribution is iteratively added to the data, progressively transforming the initial data distribution into a simple Gaussian distribution.
Probability Trajectory
Path followed by the probability distribution of data over time during the diffusion process, from the complex data distribution to the target Gaussian distribution.
Continuous Time Step
Formulation where the diffusion process is treated as a continuous phenomenon in time, allowing the use of mathematical tools like differential equations for finer analysis.
Ornstein-Uhlenbeck Process
Continuous stochastic process that pulls variables back toward their mean, often used as a forward diffusion process due to its stationarity and mean-reversion properties.
Stochastic Differential Equation (SDE)
Equation that describes the evolution of a system subject to both deterministic drift and random diffusion, forming the mathematical framework of the forward diffusion process.
Score-based Denoising
Method where the model predicts the score (gradient of the log density) at each step to guide denoising, reversing the gradient direction to remove the added noise.
Noise Schedule
Strategy defining the variance of the Gaussian noise added at each step of the diffusion process, controlling the speed and nature of the transition from the data distribution to pure noise.
Noise Prediction Network
Neural network architecture (often a U-Net) trained to predict the noise added to data at a given timestep, allowing reconstruction of the original by subtraction.
Stochastic Euler Method
Simple numerical integration scheme to approximate the solution of a stochastic differential equation, used in basic implementations of diffusion models.
Continuous Markov Chain
Stochastic process where the future state depends only on the present state and not on the past, with continuous time, modeling the gradual transition between noise states.