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Denoising Diffusion Probabilistic Model (DDPM)

Generative architecture that learns to reverse a Gaussian diffusion process, by progressively adding noise to data and then training a network to predict the added noise to reconstruct the original.

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Variance Schedule

Predefined series of variance coefficients (β_t) that control the amount of noise added at each timestep of the forward process, directly influencing the diffusion trajectory.

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Timestep

Discrete integer representing a specific step in the Markov chain of the diffusion process, ranging from clean data (t=0) to pure noise (t=T).

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Noise Prediction Network (U-Net)

Neural network architecture, typically a U-Net, used in DDPMs to predict the noise added to data at a given timestep, conditioned on that timestep.

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Langevin Sampling

Stochastic optimization method that can be used to approximate the denoising process, using score gradients to guide generation.

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Simplified Denoising Objective

DDPM loss function that simplifies training by requiring the model to directly predict the added noise, rather than the mean or covariance of the denoising distribution.

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Resampling

Inference technique where multiple denoising trajectories are explored in parallel to improve the quality and diversity of generated samples.

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Conditioning

Mechanism allowing to guide the generation process by providing additional information to the model, such as text, an image, or a class, often integrated via embeddings.

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Guided Inference

Sampling strategy that modifies the denoising process to bias generation towards desired attributes, using an external classifier (Classifier-Free Guidance) or the score gradient.

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Denoising Step

A single iteration of the reverse process where the model predicts noise and an update is applied to move from a noisy state x_t to a slightly less noisy state x_{t-1}.

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Diffusion Constant

Numerical value derived from the variance schedule, used to parameterize the evolution of data through time steps, ensuring stable convergence towards a Gaussian distribution.

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Stochastic Diffusion Equation

Stochastic differential equation that formally describes the continuous evolution of data under the effect of noise, of which the discrete DDPM process is a discretization.

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