SFA: A Statistical Physics-Inspired Diffusion Transformer for Efficient and High-Quality Image Generation

Diffusion transformers have achieved remarkable success in image generation, but accelerating attention while preserving generation quality remains a major challenge at high resolutions. Inspired by statistical physics and the widespread occurrence of scale-free laws in nature, we introduce Scale-Free Attention (SFA), which preserves fine local interactions while summarizing distant regions at progressively coarser scales. For $N$ tokens, mean pooling, token-count correction, and a shared softmax over a scale-free spatial hierarchy give SFA $O(N\log N)$ complexity in both forward and backward passes. Our Triton implementation achieves $357.3\times$ forward and $265.6\times$ backward attention speedups over FlashAttention at 262,144 tokens. After 40 epochs of PixelFlow training from scratch on ImageNet at $256\times 256$ resolution, SFA achieves the best generation quality among five attention mechanisms, including full attention. Fr\'echet inception distance evaluated on 50,000 generated samples (FID-50k) improves from 13.25 for full attention to 12.51, and the advantage over full attention persists through 80 epochs. SFA also achieves the best generation quality among the compared efficient-attention methods on Flickr-Faces-HQ (FFHQ). Beyond training from scratch, Stable Diffusion 3.5 Medium with attention replaced by SFA retains the generation quality of its full-attention counterpart under matched fine-tuning budgets. We obtain similar results when fine-tuning pretrained PixelFlow on ImageNet. SFA establishes scale-free structure as an effective design principle for efficient, high-quality diffusion transformers.