OUR SERVICE

Machine Learning

UI UX Design

Web App Development

Mobile App Development

Product Development

Offshore Partnering

Things You Need To Know To Get Started With Diffusion Models

author

Calibraint

Author

October 29, 2023

Last updated: November 29, 2023

Guide To Diffusion Models

What is a Diffusion Model?

Diffusion Models are a class of generative models that can produce realistic and diverse data, such as images, text, audio, and video. They are based on the idea of transforming the data distribution into a simple noise distribution through a series of random diffusion steps. By reversing this process, we can sample new data from the noise distribution using a learned score function that guides the diffusion towards the data distribution.

AI generated image using diffusion models

What are the advantages of Diffusion Models?

Diffusion Models have several advantages over other generative models, such as Generative Adversarial Networks (GANs) and Variational Autoencoders (VAEs). Some of these advantages are:

  • They do not suffer from mode collapse, where the stable diffusion models only generate a few modes of data distribution and ignore the rest.
  • They do not require adversarial training, which can be unstable and hard to tune.
  • They can handle discrete and continuous data without any special tricks or modifications. 
  • They can generate high-resolution and high-fidelity data with fewer parameters and less computation.

What are forward and reverse diffusion processes?

The forward and reverse diffusion processes are the core components of the Diffusion Model. They define how the data is transformed into noise and how the noise is transformed back into data.

Forward diffusion process

The forward diffusion process is a Markov chain that starts from the original data x and ends at a noise sample ε. At each step t, the data is corrupted by adding Gaussian noise to it. The noise level increases as t increases until it reaches 1 at the final step T. At this point, x_T is completely random and independent of x.

x_t = √(1 – βt) * x(t-1) + √β_t * η_t
where β_t is the noise level at step t, and η_t is a standard Gaussian random variable. The noise level β_t increases as t increases until it reaches 1 at the final step T. At this point, x_T is completely random and independent of x.

Reverse diffusion process

The reverse diffusion process is the inverse of the forward diffusion process. It starts from a noise sample ε and ends at a data sample x. At each step t, the noise is reduced by subtracting Gaussian noise from it. The noise level decreases as t decreases until it reaches 0 at the initial step 0. At this point, ε0 is equal to x.

ε_t = √(1 – β_t) * ε(t+1) – √β_t * η_t

where β_t is the same noise level as in the forward diffusion process, and η_t is a standard Gaussian random variable. The noise level β_t decreases as t decreases until it reaches 0 at the initial step 0. At this point, ε_0 is equal to x.

Denoising process

How to set up the forward and reverse diffusion processes?

In practice, we do not know the exact value of ηt at each step. Therefore, we need a score function s_t(x_t) that estimates the conditional distribution of x(t-1) given x_t. The score function s_t(x_t) tells us how likely x_(t-1) is for a given x_t, and how to adjust x_t to make it closer to x_(t-1). We can use the score function s_t(x_t) to sample from the reverse diffusion process using Langevin dynamics:

x_(t-1) = x_t + α_t * s_t(x_t) + √(2 * α_t) * ζ

where α_t is the step size at step t, and ζ is a standard Gaussian random variable. By repeating this process from t = T to t = 0, we can generate a data sample x from a noise sample ε.

How to choose the noise schedule and the number of steps?

The noise schedule and the number of steps are two important hyperparameters that affect the performance of the Diffusion Model. They determine how fast and how smoothly the data is transformed into noise and vice versa.

The noise schedule is a sequence of noise levels β_t that control the amount of Gaussian noise added or subtracted at each step t. A common choice for the noise schedule is to use a geometric progression:

β_t = β * (1 – β)^(T – 1 – t)

where β is a constant between 0 and 1, and T is the total number of steps. This noise schedule ensures that the variance of x_t is constant for all t, which simplifies the score function estimation.

The number of steps T is the length of the forward and reverse diffusion processes. It affects the quality and diversity of the generated data. A larger T means that the data is more corrupted by noise, which makes it harder to recover from the noise, but also allows for more variation in the data. A smaller T means that the data is less corrupted by noise, which makes it easier to recover from the noise, but also limits the variation in the data.

There is a trade-off between the noise schedule and the number of steps. A more aggressive noise schedule (larger β) requires more steps to achieve better quality, while a less aggressive noise schedule (smaller β) requires fewer steps to achieve good diversity. The optimal choice of these hyperparameters depends on the data domain, the score function architecture, and the computational budget.

Note:

β is a constant between 0 and 1 that controls the noise level in the Diffusion Model. A larger β means that more noise is added or subtracted at each step, while a smaller β means that less noise is added or subtracted at each step. A larger β makes the data more corrupted by noise, while a smaller β makes the data less corrupted by noise.

0.5 is the middle value of β and is neither considered as a small nor a large β. It is a middle value of β that balances the trade-off between quality and diversity in the Diffusion Model. It means that the noise level is 50% at the final step of the forward diffusion process and 50% at the initial step of the reverse diffusion process. It is a balanced choice that preserves some information and some variation in the data. 

However, it may not be the optimal choice for every data domain or score function architecture. You may need to experiment with different values of β to find the best one for your task. 

How to train a Diffusion Model

To sample from the trained Diffusion Model, we need to follow the reverse diffusion process using the score function and Langevin dynamics. 

Here are the steps to do that:

  1. Start from a random noise sample ε ~ N(0, I), where I is the identity matrix.
  1. Set t = T, where T is the total number of steps in the forward and reverse diffusion processes.
  1. While t > 0, do the following:
  1. Compute the score function output s_t(x_t) by feeding x_t to the neural network.
  1. Update x_(t-1) by using the Langevin dynamics formula:

x_(t-1) = x_t + α_t * s_t(x_t) + √(2 * α_t) * ζ

where α_t is the step size at step t, and ζ is a standard Gaussian random variable.

  1. Decrease t by 1. 
  2. Return x_0 as the sampled data.

Final note

Diffusion Model in AI is a promising research direction in the field of generative AI modeling. They have shown impressive results in various data domains, such as images, text, audio, and video. Applications of diffusion models can be found in areas such as data augmentation, super-resolution, inpainting, style transfer, and more. 

However, there are still some challenges and limitations that need to be addressed in the future. Experts are working on solutions to overcome the challenges and improve its results but until then Happy Diffusing readers.

Related Articles

field image

NFTs are digital assets that have a unique identity recorded in blockchain. NFTs can represent anything that is digital, such as art, music, videos, games, or even tweets, its use cases are endless. Unlike other digital files, which can be copied and shared endlessly, NFTs have a special feature: they are non-fungible making them one […]

author-image

Calibraint

Author

16 Nov 2023

field image

Have you ever wondered how much AI is changing the eCommerce web development sector? Its impact on our world is quite evident as we are witnessing several new platforms on a regular basis. AI is helping eCommerce web developers to create more user-friendly, personalized, and efficient websites that can boost sales and customer satisfaction. What […]

author-image

Calibraint

Author

11 Oct 2023

field image

Computers can do many things, but can they see? Can they understand what they see? Can they help us with things that need vision, like security, healthcare, entertainment, education, and more? Computer vision in AI teaches systems to deal with visual information and extract information from them. It is a field that makes computers see […]

author-image

Calibraint

Author

29 Sep 2023

field image

We all have been a victim of online fraud at some point in our lives. It has been on the rise ever since eCommerce giants stepped in and the onset of COVID-19 pushed it further. The substantial growth in the last few years has given rise to online fraud in proportion to this growth. Experts […]

author-image

Vishaal

25 Sep 2023

field image

AI Safety and Alignment : Here Is What You Need To Know! Unless you are a Luddite or an ardent follower of Neo-Luddism, you are already using AI-based services every day. Also, if you are a fan of the science fiction genre, you’d be curious about how AI will change the world. Either way, you […]

author-image

Vishaal

05 Sep 2023

field image

AI is one of the most fascinating and influential technologies of our time. Artificial intelligence applications can potentially transform many aspects of our society and economy by creating new opportunities and solutions for various challenges. AI can also enhance our capabilities and experiences by providing us with smart tools and services that can assist us […]

author-image

Vishaal

01 Sep 2023

Let's Start A Conversation

Table of Contents