Accelerating and Privatizing Diffusion Models

Abstract

Diffusion models (DMs) have emerged as a powerful class of generative models. DMs offer both state-of-the-art synthesis quality and sample diversity in combination with a robust and scalable learning objective. DMs rely on a diffusion process that gradually perturbs the data towards a normal distribution, while the neural network learns to denoise. Formally, the problem reduces to learning the score function, i.e., the gradient of the log-density of the perturbed data. The reverse of the diffusion process can be approximated by a differential equation, defined by the learned score function, and can therefore be used for generation when starting from random noise. In this thesis, we give a thorough and beginner-friendly introduction to DMs and discuss their history starting from early work on score-based generative models. Furthermore, we discuss connections to other statistical models and lay out applications of DMs, with a focus on image generative modeling.

We then present CLD: a new DM based on critically-damped Langevin dynamics. CLD can be interpreted as running a joint diffusion in an extended space, where the auxiliary variables can be considered "velocities" that are coupled to the data variables as in Hamiltonian dynamics. We derive a novel score matching objective for CLD-based DMs and introduce a fast solver for the reverse diffusion process which is inspired by methods from the statistical mechanics literature. The CLD framework provides new insights into DMs and generalizes many existing DMs which are based on overdamped Langevin dynamics.

Next, we present GENIE, a novel higher-order numerical solver for DMs. Many existing higher-order solvers for DMs built on finite difference schemes which break down in the large step size limit as approximations become too crude. GENIE, on the other hand, learns neural network-based models for higher-order derivatives whose precision do not depend on the step size. The additional networks in GENIE are implemented as small output heads on top of the neural backbone of the original DM, keeping the computational overhead minimal. Unlike recent sampling distillation methods that fundamentally alter the generation process in DMs, GENIE still solves the true generative differential equation, and therefore naturally enables applications such as encoding and guided sampling.

The fourth chapter presents differentially private diffusion models (DPDMs), DMs trained with strict differential privacy guarantees. While modern machine learning models rely on increasingly large training datasets, data is often limited in privacy-sensitive domains. Generative models trained on sensitive data with differential privacy guarantees can sidestep this challenge, providing access to synthetic data instead. DPDMs enforce privacy by using differentially private stochastic gradient descent for training. We thoroughly study the design space of DPDMs and propose noise multiplicity, a simple yet powerful modification of the DM training objective tailored to the differential privacy setting. We motivate and show numerically why DMs are better suited for differentially private generative modeling than one-shot generators such as generative adversarial networks or normalizing flows.

Finally, we propose to distill the knowledge of large pre-trained DMs into smaller student DMs. Large-scale DMs have achieved unprecedented results across several domains, however, they generally require a large amount of GPU memory and are slow at inference time, making it difficult to deploy them in real-time or on resource-limited devices. In particular, we propose an approximate score matching objective that regresses the student model towards predictions of the teacher DM rather than the clean data as is done in standard DM training. We show that student models outperform the larger teacher model for a variety of compute budgets. Additionally, the student models may also be deployed on GPUs with significantly less memory than was required for the original teacher model.