Concept Glossary

The adhesion of atoms, ions, or molecules to a surface. Distinct from absorption, where a substance penetrates into the bulk of a material. Adsorption often accompanies diffusion at interfaces.

The random, erratic movement of particles suspended in a fluid, caused by collisions with the fluid's molecules. Einstein's 1905 analysis of Brownian motion provided early evidence for the existence of atoms.

A difference in the concentration of a substance across a spatial region. Diffusion occurs down a concentration gradient — from regions of high concentration to low — until equilibrium is reached.

Denoising Diffusion Probabilistic Model. A class of generative AI models that learn to reverse a gradual noising process. The model is trained to predict and remove noise at each step, enabling generation from pure noise.

The process of removing noise from a signal. In diffusion models, the network learns to denoise — predict the clean signal given a noisy version. The entire generative process is iterative denoising.

A proportionality constant (D) in Fick's laws that quantifies how quickly a substance diffuses through a medium. It depends on temperature, the size of the diffusing particles, and the viscosity of the medium.

The state in which a concentration gradient has been eliminated and net diffusion ceases. Individual particles still move randomly, but there is no net flow in any direction.

States that the diffusion flux is proportional to the negative of the concentration gradient: J = -D(∂C/∂x). Particles flow from high concentration to low, at a rate determined by the diffusion coefficient.

Predicts how the concentration changes over time due to diffusion: ∂C/∂t = D(∂²C/∂x²). It describes how concentration profiles evolve and spread out, forming the basis of diffusion equation.

A partial differential equation describing the time evolution of the probability density function of a particle undergoing drift and diffusion. It generalizes the diffusion equation to include deterministic forces.

Random noise drawn from a normal (Gaussian) distribution. In diffusion models, Gaussian noise is progressively added to data during the forward process and predicted/removed during the reverse process.

A diffusion model that operates in a compressed latent space rather than pixel space. Stable Diffusion uses this approach — diffusing and denoising in a lower-dimensional representation for efficiency.

A stochastic process where the next state depends only on the current state, not on the history. The forward and reverse processes in diffusion models are formulated as Markov chains.

The diffusion of water across a semi-permeable membrane from a region of low solute concentration to high solute concentration. A specialized case of diffusion that is critical to biological function.

In AI diffusion models, the learned process of gradually removing noise to generate data. It approximates the reversal of the forward noising process, step by step, from pure noise to a coherent sample.

A training technique where a model learns the gradient of the log-probability density (the "score") of a data distribution. Score-based diffusion models use this to guide the reverse denoising process.

A barrier that allows certain molecules to pass through while blocking others. In biology, cell membranes are semi-permeable, allowing selective diffusion of water and specific solutes.

The random movement of particles due to thermal energy. At any temperature above absolute zero, particles possess kinetic energy and move randomly — this is the physical driver of diffusion in fluids.

A neural network architecture with an encoder-decoder structure and skip connections, shaped like the letter U. Most diffusion models use a UNet as the denoising backbone.

A measure of how spread out a set of values is. In diffusion, variance quantifies how much a particle's position spreads over time — it increases linearly with time in simple diffusion (Einstein's relation).