Diffusion Model

What is diffusion model

• Diffusion models are a class of mathematical models used to describe how particles or information spread over time in a medium (e.g., physical space, social networks, etc.)

mathematical representation

where:

• $x(t)$ is the state variable (e.g., accumulated evidence)
• $D$ is the diffusion coefficient
• $W(t)$ is a Wiener process (representing random noise)

key feature

• stochastic: the process is inherently random

Application of diffusion models

in cognitive science

• decision-making
  • diffusion models describe the accumulation of evidence over time as a stochastic process. The decision is made when the accumulated evidence reaches a certain threshold.
  • also see Drift Diffusion Model#in cognitive science

in deep learning/AI

• diffusion process is useful for generative models to create new data by starting from noise and refining it into a meaningful output
  • forward process
    • it is a diffusion process where noise is incrementally added to the data at each step
    • this gradual corruption transforms the data into pure noise
  • reverse process
    • it is a diffusion process that denoises the data step by step
    • this reverses the noise addition and reconstructs the original or new data from the noisy latent representation
• examples
  • latent diffusion model
    • it operate in a compressed latent space instead of the original data space, making them computationally more efficient while still producing high-quality outputs
    • the diffusion process (i.e., adding and then reversing noise) is applied within this latent space, allowing the model to learn and generate high-quality data with less computational expense
  • stable diffusion model
    • a specific implementation of a latent diffusion model
    • a type of LDM designed for tasks like generating images, text, or other types of data from prompts or initial inputs

Diffusion model vs. Drift diffusion model

The Drift Diffusion Model is an extension of the diffusion model, specifically tailored for modeling decision-making processes and with a drift component to the diffusion process.