What is the role of momentum in optimizing diffusion models?

Momentum plays a key role in optimizing diffusion models by improving the stability and speed of the training process. In diffusion models, the goal is to train a neural network to reverse a gradual noising process, which requires solving a sequence of complex optimization problems. Momentum, a technique borrowed from optimization algorithms like stochastic gradient descent (SGD), helps manage the noisy and high-variance gradients that arise during training. By accumulating a weighted average of past gradients, momentum smooths out abrupt changes in update directions, allowing the model to converge faster and avoid getting stuck in local minima or oscillating around optimal parameters.

A concrete example of momentum’s impact is in the training of Denoising Diffusion Probabilistic Models (DDPMs). These models predict noise at each timestep of the diffusion process, and their loss landscapes can be irregular due to the varying levels of noise added across timesteps. Without momentum, gradient updates might overshoot or fluctuate excessively, especially when dealing with timesteps where the noise structure changes rapidly. Momentum mitigates this by introducing inertia into the parameter updates. For instance, when using an optimizer like Adam (which includes momentum-like terms via exponential moving averages), the model can maintain a steadier trajectory toward the optimum, even when individual gradient estimates are noisy. This is particularly useful in later stages of training, where fine-grained adjustments are necessary to refine the model’s output quality.

From an implementation perspective, momentum parameters (e.g., β₁ in Adam) are often tuned to balance short-term and long-term gradient information. In diffusion models, a common choice is β₁=0.9, which weights recent gradients more heavily while still retaining some historical context. This setup helps the model adapt to the time-dependent nature of the diffusion process—where gradients for early timesteps (heavy noise) differ significantly from later ones (subtle refinements). Developers can experiment with these hyperparameters to optimize training stability; for example, reducing β₁ might help in scenarios where the gradient distribution shifts abruptly between timesteps. Overall, momentum acts as a stabilizing force, making the optimization of diffusion models more efficient and reliable without introducing significant computational overhead.