Denoising Diffusion Implicit Models (DDIMs): Fast Sampling and Inversion for Generative Models

Denoising Diffusion Implicit Models (DDIMs) are an extension of Denoising Diffusion Probabilistic Models (DDPMs) that address two key limitations: slow sampling speed and lack of inversion capabilities. DDIMs maintain the same training procedure as DDPMs but modify the inference process to enable faster sampling and exact inversion.

Motivation for DDIMs

There are two main motivations for developing DDIMs:

1. Slow sampling in DDPMs: The sampling process in DDPMs requires hopping through T steps (typically thousands) from the noise distribution to the data distribution. This makes inference slow, especially for high-resolution images.

2. Lack of inversion in DDPMs: DDPMs cannot perform posterior inference or inversion. Given an input sample, there's no guarantee that encoding it to the latent space and then decoding will produce the exact same sample.

DDIMs aim to solve both these issues by introducing non-Markovian models that enable fast sampling and inversion capabilities.

Key Insights of DDIMs

The key insights behind DDIMs are:

1. The DDPM loss function depends only on q(x_t|x_0), not on the full joint distribution q(x_1:T|x_0).

2. Multiple joint distributions can have the same conditional distribution.

Based on these insights, DDIMs define a family of non-Markovian encoding distributions that have the same conditional distribution as DDPMs.

Non-Markovian Forward Process

DDIMs define a non-Markovian forward process q_σ(x_1:T|x_0) as follows:

q_σ(x_1:T|x_0) = q_σ(x_T|x_0) ∏ q_σ(x_t-1|x_t, x_0)

where q_σ(x_t-1|x_t, x_0) is a Gaussian distribution with a specific mean and variance.

This formulation ensures that q_σ(x_t|x_0) matches the conditional distribution of DDPMs.

Reverse Process

The reverse (denoising) process is defined similarly to DDPMs, but with modified mean and variance terms to account for the non-Markovian nature of the forward process.

Training and Inference

The key advantage of DDIMs is that they can be trained using the exact same procedure and loss function as DDPMs. This means that when you train a DDPM, you're implicitly training a large class of non-Markovian models (DDIMs) as well.

However, the inference procedures differ:

• In DDPMs, sampling involves recursively applying the reverse process p_θ(x_t-1|x_t).
• In DDIMs, sampling uses a modified reverse process with different mean and variance terms.

Inversion Capabilities

By setting σ=0 in the DDIM formulation, we get a deterministic encoding process. This enables exact inversion:

1. Given an input x_0, run the deterministic forward process to get x_T.
2. Run the DDIM reverse process starting from x_T.
3. This will produce exactly the same x_0 we started with.

This inversion capability is not possible with standard DDPMs.

Advantages of DDIMs

1. Faster sampling: The non-Markovian nature of DDIMs allows for faster sampling by taking larger steps in the reverse process.

2. Inversion capabilities: DDIMs enable exact inversion, which is useful for tasks like latent space interpolation and editing.

3. No additional training: DDIMs can be used with pre-trained DDPM models without any modification or retraining.

Applications

DDIMs have found applications in various state-of-the-art text-to-image generation models. They are often used in conjunction with classifier-free guidance for conditional generation tasks.

Conclusion

Denoising Diffusion Implicit Models (DDIMs) represent a significant advancement in the field of generative modeling. By addressing the limitations of DDPMs while maintaining their training simplicity, DDIMs have become a popular choice for many applications, especially in the domain of text-to-image generation.

The ability to perform fast sampling and exact inversion makes DDIMs particularly attractive for real-world applications where inference speed and precise control over the generation process are crucial. As research in this area continues to evolve, we can expect to see further refinements and applications of DDIM-based models in various domains of machine learning and artificial intelligence.

Article created from: https://youtu.be/chJt2HEwuwU?feature=shared