The state of the art for generating complex data such as images, sounds or complex physical fields is the diffusion score algorithm. The score diffusion algorithm samples a probability distribution by transporting white Gaussian noise to the distribution to be sampled, using a stochastic differential equation. The starting point is the Ornstein-Uhlenbeck equation, which progressively adds white noise to a sample of the probability distribution. The diffusion score equation inverts this equation, gradually removing the noise that has been added. This is calculated with a stochastic diffusion score equation. The derivative term of this equation is the score (gradient of the log-probability) of the distribution of noisy samples. The main difficulty is to calculate this score.
The Robbins, Tweetie, Myasawa equation shows that the score can be used to calculate an optimal estimator of a sample to which white noise has been added. A deep neural network is used to optimize the denoising of samples from a training database. This enables the score to be estimated at all noise levels. Diffusion scoring algorithms provide excellent results for generating images, sounds and all kinds of complex data, using neural networks.
