How to Use Stable Diffusion for Better Image Processing

Image processing is a broad field that encompasses many techniques and applications, such as enhancing, compressing, restoring, segmenting, and analyzing images. One of the fundamental tools in image processing is diffusion, which is a process of smoothing or blurring an image by spreading out the pixel values over a neighborhood.

Diffusion can be useful for many purposes, such as reducing noise, enhancing edges, or creating artistic effects. However, not all diffusion methods are created equal. Some diffusion methods can introduce artifacts or distortions in the image, such as overshooting, ringing, or staircasing. These artifacts can degrade the quality and usability of the image.

One way to avoid these artifacts is to use stable diffusion, which is a class of diffusion methods that preserve the essential features and structures of the image while smoothing out the unwanted details. Stable diffusion methods are based on the idea of minimizing a certain energy functional that measures the smoothness and fidelity of the image. By using a suitable energy functional and a numerical scheme, stable diffusion methods can achieve a balance between smoothing and preserving the image.

In this blog post, we will introduce some of the basic concepts and principles of stable diffusion methods, and show some examples of how they can be applied to different image processing tasks. We will also provide some code snippets and resources for implementing stable diffusion methods in Python.

What is Stable Diffusion?

Stable diffusion is a general term that refers to a family of diffusion methods that have certain desirable properties and characteristics. Some of these properties are:

One way to understand stable diffusion is to compare it with linear diffusion, which is a simple and classical diffusion method that follows the heat equation:

$$\frac{\partial u}{\partial t} = \Delta u$$

where $u$ is the image intensity function, $t$ is the time parameter, and $\Delta$ is the Laplacian operator. Linear diffusion can be interpreted as applying a Gaussian filter to the image with a standard deviation proportional to $\sqrt{t}$. This means that linear diffusion smooths out the image uniformly and isotropically, regardless of the image features or structures.

Linear diffusion has some advantages, such as being easy to implement and fast to compute. However, it also has some drawbacks, such as being prone to blurring edges and creating artifacts. For example, consider the following image:

ayaka from Genshin Impact

If we apply linear diffusion to this image for different values of $t$, we get the following results:

ayaka from Genshin Impact

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As we can see, linear diffusion smooths out the noise in the background, but also blurs out the edges and details in the foreground. Moreover, linear diffusion introduces some artifacts in the image, such as overshooting (the bright halo around the dark object) and staircasing (the blocky appearance of the gradient regions).

To overcome these drawbacks, stable diffusion methods use a nonlinear modification of the linear diffusion equation:

$$\frac{\partial u}{\partial t} = \text{div}(g(\nabla u)\nabla u)$$

where $\text{div}$ is the divergence operator, $\nabla$ is the gradient operator, and $g$ is a nonlinear function that depends on the magnitude of $\nabla u$. The function $g$ is called the diffusivity function or edge-stopping function, and it controls how much diffusion occurs at each point of the image. The idea is to use a function $g$ that is small when $\nabla u$ is large (i.e., at edges or boundaries), and large when $\nabla u$ is small (i.e., at smooth or homogeneous regions). This way, the diffusion process can preserve or enhance the edges, and many more.

Stable Diffusion: Advantages and Disadvantages

Stable diffusion is a novel technique for generating realistic and diverse images from text prompts. It is based on latent diffusion models, which are a type of generative model that learn to synthesize images by gradually adding noise and then removing it. Stable diffusion is an open-source project developed by Stability.ai and Runway ML, and it has attracted a lot of attention from the AI community and the general public for its impressive results and accessibility.

Advantages of Stable Diffusion

Disadvantages of Stable Diffusion