Understanding Prediction Target, Time Sampling, and Model Capacity in Diffusion Models

Denoising diffusion models require several coupled design choices: what the network predicts, how timesteps are sampled, and how much capacity the architecture provides. Three recent empirical findings shed light on how to make these choices: (i) clean data prediction can have higher generation quality than noise or velocity prediction; (ii) sampling timesteps from a logit-normal distribution can outperform uniform sampling; and (iii) generation quality can peak at an intermediate model capacity. However, a theoretical understanding of these observations, and particularly of how the three choices interact, remains limited. In this paper, we show that theoretical counterparts of all three observations arise in a tractable linear model with Gaussian data and a time-gated predictor. Specifically, our spectral analysis reveals how prediction targets, timestep sampling, and model capacity jointly determine which spectral components of the data are represented by the model and, in turn, shape the generated distribution, a principle we refer to as spectral selection. This analysis further shows that the optimal design choices depend on the spectral structure of the data. We provide empirical support for our theoretical findings on synthetic and real data.