DMDA: Density Matrix Decomposition for Training-Free Diffusion Acceleration

We present the Density Matrix Diffusion Accelerator (DMDA), a training-free inference acceleration framework for sequential diffusion generation. The core insight is that density matrix eigendecomposition of diffusion latent sequences reveals extreme spectral concentration — a single shared eigenmode captures the majority of total latent energy — enabling selective computation in which the shared component is processed fully only once, while per-frame perturbations are handled via lightweight residual diffusion. We validate DMDA on two architecturally distinct models on a Mac Studio M2 Ultra (MPS backend). On Stable Diffusion 1.5 (860M parameters, 512×512), DMDA achieves 9.4× step reduction (1,500 → 160 steps, 35.25s wall-clock) with dominant eigenvalue λ₁ = 0.8576 (85.76% energy). On SDXL (2.6B parameters, 1024×1024, dual text encoder), DMDA achieves 5.1× step reduction (750 → 146 steps, 151.1s wall-clock) with λ₁ = 0.7093 (70.93% energy). In both cases, generated frames exhibit visual quality equivalent to standard outputs with no perceptible degradation. DMDA is training-free, architecture-agnostic, and requires no modification to model weights or architecture. It operates on a different computational axis from existing methods — reducing inter-frame redundancy rather than per-frame step count — and composes multiplicatively with distillation-based approaches.