Binxu Wang
Publications
A Random Matrix Theory Perspective on the Consistency of Diffusion Models
Diffusion models trained on different, non-overlapping subsets of a dataset often produce strikingly similar outputs when given the same noise seed. We trace this consistency to a simple linear effect: the shared Gaussian statistics across splits already predict much of the generated images. To formalize this, we develop a random matrix theory (RMT) framework that quantifies how finite datasets shape the expectation and variance of the learned denoiser and sampling map in the linear setting. For expectations, sampling variability acts as a renormalization of the noise level through a self-consistent relation $σ^2 \mapsto κ(σ^2)$, explaining why limited data overshrink low-variance directions and pull samples toward the dataset mean. For fluctuations, our variance formulas reveal three key factors behind cross-split disagreement: \textit{anisotropy} across eigenmodes, \textit{inhomogeneity} across inputs, and overall scaling with dataset size. Extending deterministic-equivalence tools to fractional matrix powers further allows us to analyze entire sampling trajectories. The theory sharply predicts the behavior of linear diffusion models, and we validate its predictions on UNet and DiT architectures in their non-memorization regime, identifying where and how samples deviates across training data split. This provides a principled baseline for reproducibility in diffusion training, linking spectral properties of data to the stability of generative outputs.
Circuit Mechanisms for Spatial Relation Generation in Diffusion Transformers
Diffusion Transformers (DiTs) have greatly advanced text-to-image generation, but models still struggle to generate the correct spatial relations between objects as specified in the text prompt. In this study, we adopt a mechanistic interpretability approach to investigate how a DiT can generate correct spatial relations between objects. We train, from scratch, DiTs of different sizes with different text encoders to learn to generate images containing two objects whose attributes and spatial relations are specified in the text prompt. We find that, although all the models can learn this task to near-perfect accuracy, the underlying mechanisms differ drastically depending on the choice of text encoder. When using random text embeddings, we find that the spatial-relation information is passed to image tokens through a two-stage circuit, involving two cross-attention heads that separately read the spatial relation and single-object attributes in the text prompt. When using a pretrained text encoder (T5), we find that the DiT uses a different circuit that leverages information fusion in the text tokens, reading spatial-relation and single-object information together from a single text token. We further show that, although the in-domain performance is similar for the two settings, their robustness to out-of-domain perturbations differs, potentially suggesting the difficulty of generating correct relations in real-world scenarios.