Stable Diffusion is a machine learning algorithm that can be used for image denoising, inpainting, and super-resolution. The algorithm is based on the diffusion process, where the heat equation is used to model the process of heat transfer in a material. The algorithm is called "stable" because it avoids numerical instabilities that can arise when solving the heat equation.

Stable Diffusion works by modeling the image as a diffusion process, where the pixels of the image are considered as points in a high-dimensional space. The algorithm then applies a diffusion process to these points, which smooths out the image while preserving its important features. The diffusion process is guided by a regularization parameter that controls the level of smoothing applied to the image.

The algorithm is applied iteratively to the image until convergence, meaning that the image no longer changes significantly with each iteration. At each iteration, the algorithm applies a partial differential equation to the image, which is derived from the heat equation. The equation describes how the image should diffuse over time, while ensuring that the solution remains stable and does not become too smooth.

Stable Diffusion has several advantages over other image processing algorithms. It is a non-linear algorithm that can handle complex image structures, and it is computationally efficient, making it suitable for real-time image processing applications. Additionally, it is a parameter-free algorithm, meaning that the user does not need to tune any parameters to get good results.