# What are Diffusion Models?

TLDRDiffusion models are a breakthrough in generative modeling, using a process that adds and then gradually removes noise to generate high-quality images. They've shown to outperform GANs in certain tasks and can adapt to various settings like text-to-image conversion. The script explains the mechanics of diffusion models, including the forward and reverse processes, the variational lower bound for training, and conditional sampling techniques. These models are gaining attention for their potential in image generation and manipulation.

### Takeaways

- ๐ Diffusion models are a type of generative model that can reverse the process of adding noise to an image, resulting in a coherent image from pure noise.
- ๐ They have gained significant traction and are rivaling other generative models like GANs in image generation tasks.
- ๐ The forward diffusion process gradually adds noise to an image over time steps, while the reverse process learns to remove the noise step by step.
- ๐ The variance of the noise added at each step is typically a hyperparameter that increases with time, bringing the mean of each new Gaussian closer to zero.
- ๐ง The reverse process is modeled as a Markov chain, with each step parameterized as a unimodal diagonal Gaussian, making it easier to learn.
- ๐ The training objective is not a direct maximum likelihood objective but a lower bound, which is optimized by maximizing the conditional density of the reverse steps.
- ๐ค The reverse process network is tasked with learning the means of the Gaussian distributions for each step, using a reparameterization technique.
- ๐ Diffusion models can be adapted for conditional generation, such as converting text descriptions to images, by incorporating additional inputs during training.
- ๐จ For tasks like inpainting, fine-tuning the model on images with randomly removed sections can lead to better results than using a standard model.
- ๐ There is a connection between diffusion models and score matching models, where the score can be shown to be equivalent to the noise predicted in the diffusion objective.
- ๐ Diffusion models have shown promising results in density estimation benchmarks and are gaining momentum in the field of generative modeling.

### Q & A

### What is the basic concept behind diffusion models?

-Diffusion models are based on the idea of starting with a noise image and gradually removing the noise to end up with a coherent image. They are a type of generative model that has shown success in image generation and can rival or surpass other generative models like GANs in certain tasks.

### How do diffusion models compare to GANs in terms of performance?

-Diffusion models have outperformed GANs in perceptual quality metrics and have shown impressive performance in various conditional settings such as converting text descriptions to images, inpainting, and manipulation.

### What is the forward diffusion process in diffusion models?

-The forward diffusion process gradually adds noise to the image over a series of time steps, essentially pushing a sample off the data manifold, turning it into noise. This process is designed to be a Markov chain where the distribution at a particular time step only depends on the sample from the immediately previous step.

### What is the reverse process in diffusion models, and how does it differ from the forward process?

-The reverse process is tasked with starting from a noisy image and undoing the noise through a learned process. Unlike the forward process, which is typically fixed, the reverse process is what the model learns to perform, aiming to produce a trajectory back to the data manifold and resulting in a reasonable sample.

### Why is a small step size beneficial in the forward diffusion process?

-A small step size in the forward diffusion process reduces ambiguity about the previous step of the Markov chain, making it easier for the model to learn to undo the steps. It allows the model to use a unimodal Gaussian to model the posterior of the forward step, simplifying the learning process.

### How does the model account for the forward process variance schedule in the reverse process?

-The model takes the time step 't' as input to account for the forward process variance schedule. Different time steps are associated with different noise levels, and the model learns to undo these individually.

### What is the objective of training a diffusion model?

-The objective of training a diffusion model is to maximize a lower bound, known as the variational lower bound or evidence lower bound, on the marginal log-likelihood of the data. This involves maximizing a likelihood term and minimizing a KL divergence term.

### How does the training objective of diffusion models relate to that of variational autoencoders (VAEs)?

-The training objective of diffusion models borrows from VAEs, using a variational lower bound that includes a likelihood term and a KL divergence term. The forward process in diffusion models is analogous to the encoder in VAEs, and the reverse process is analogous to the decoder.

### What are some challenges and solutions for conditional sampling with diffusion models?

-Conditional sampling with diffusion models can be achieved by feeding the conditioning variable as an additional input during training. However, relying on a separate classifier can be a drawback. Alternative approaches include special training of the diffusion model to guide sampling without the need for a second network.

### How do diffusion models perform in tasks like inpainting?

-Diffusion models can perform inpainting by fine-tuning a model specifically for this task, where sections of training images are randomly removed and the model attempts to fill them in conditioned on the full clear context. This approach has been shown to produce better results than using a standard-trained model.

### What is the relationship between diffusion models and score matching models?

-There is a close connection between denoising diffusion models and score matching models. The score, which is the gradient of the log of the target probability density with respect to the data, can be shown to be equivalent to the noise predicted in the denoising diffusion objective, up to a scaling factor.

### Outlines

### ๐ Introduction to Diffusion Models

This paragraph introduces the concept of diffusion models in generative modeling. It explains the idea of adding Gaussian noise to an image repeatedly until it becomes unrecognizable, and then reversing this process to recover the original image from pure noise. This approach has been successful in image generation, outperforming GANs in certain tasks and showing promise in converting text to images and image manipulation. The paragraph sets the stage for understanding the basic mechanism of diffusion models and their adaptability to various generative settings.

### ๐ The Forward and Reverse Diffusion Processes

This section delves into the technical details of the forward and reverse diffusion processes. The forward process gradually adds noise to an image over time steps, described as a Markov chain, with the distribution at each step depending only on the previous sample. The reverse process is the model's task to undo this noise addition, starting from a noisy image and aiming to recover the original data. The benefits of using small step sizes in the forward process are discussed, along with the theoretical justification for modeling the reverse process as a unimodal Gaussian, similar to the forward process.

### ๐ Training Objectives and Variational Lower Bound

The paragraph explains the training objectives for diffusion models, which involve maximizing a lower bound to the marginal log-likelihood of the data. It draws parallels with variational autoencoders (VAEs), where the forward process is analogous to the encoder and the reverse process to the decoder. The training objective is derived from the variational lower bound, which includes a likelihood term and a KL divergence term. The paragraph also discusses the challenges in optimizing this objective due to high variance and presents a rearranged objective to improve training efficiency.

### ๐ ๏ธ Implementations and Conditional Sampling

This paragraph discusses various implementations of the reverse step in diffusion models and the techniques for conditional sampling. It covers the use of time-specific constants for reverse process variances and the prediction of noise instead of Gaussian mean. The paragraph also explores different approaches for conditional generation, such as feeding a conditioning variable during training or using a separate classifier to guide the diffusion process. Additionally, it touches on the application of diffusion models to inpainting tasks and compares diffusion models with other generative models like GANs and score matching models.

### ๐ Conclusion and Future of Diffusion Models

In conclusion, the paragraph highlights the momentum and progress of diffusion models in the field of generative modeling. It emphasizes the potential of these models, as evidenced by their competitive performance in density estimation benchmarks and their connection to score matching models. The paragraph ends with an invitation to explore further resources on the topic, showcasing the excitement around the development and application of diffusion models.

### Mindmap

### Keywords

### ๐กDiffusion Models

### ๐กGaussian Noise

### ๐กMarkov Chain

### ๐กVariance

### ๐กReverse Process

### ๐กLatent Variables

### ๐กVariational Autoencoders (VAEs)

### ๐กEvidence Lower Bound (ELBO)

### ๐กInpainting

### ๐กConditional Generation

### Highlights

Diffusion models are a type of generative model that can reverse the process of adding noise to an image, starting from pure noise and gradually removing it to produce a coherent image.

These models have been successful in image generation, rivaling and sometimes surpassing other generative models like GANs in perceptual quality metrics.

Diffusion models have shown impressive performance in conditional settings such as converting text descriptions to images and image manipulation.

The forward diffusion process adds noise to an image over time steps, while the reverse process is tasked with undoing this noise to recover the original image.

The forward process is modeled as a Markov chain, with each step's distribution depending only on the previous step's sample.

Variance parameters in the diffusion process are typically hyperparameters that follow a fixed schedule, increasing with time and restricted between zero and one.

Using a small step size in the diffusion process makes learning to undo the steps less difficult and reduces ambiguity about the previous step.

The reverse process is modeled as a Markov chain as well, with the model learning to undo the noise individually at each time step.

The reverse process takes time as input to account for the forward process variance schedule and can learn to undo different noise levels.

Diffusion models are trained to maximize a lower bound on the marginal log-likelihood, using a variational lower bound similar to that used in VAEs.

The training objective combines a likelihood term that encourages the model to maximize the density assigned to the data with a KL divergence term.

The KL divergence term encourages the approximate posterior to be similar to the prior on the latent variable.

The reverse step in diffusion models is parameterized as a unimodal diagonal Gaussian, leveraging the observation that the true reverse process will have the same functional form as the forward process.

Diffusion models can be made to sample conditionally given some variable of interest, such as a class label or a sentence description.

Classifier guidance can be used to push the reverse diffusion process in the direction of the gradient of the target label probability with respect to the current noise image.

Inpainting with diffusion models involves fine-tuning a model specifically for this task, rather than using a standard-trained model.

Diffusion models can be compared to other generative models like GANs, with each having its own advantages and limitations.

Continuous time formulations of diffusion models can give rise to probability flow ODEs, enabling log-likelihood approximation via numerical integration.

There is a close connection between denoising diffusion models and score matching models, with the score being equivalent to the noise predicted in the denoising diffusion objective.

Diffusion models are gaining momentum and showing promising progress in the field of generative modeling.