Joint Branch-Space Transform Coding for Diffusion Activation Quantization with Classifier-Free Guidance

Post-training quantization for diffusion models increasingly exploits timestep, feature, and layer structure. While recent work has begun incorporating CFG structure into diffusion quantization, activation quantization still operates independently across conditional and unconditional coordinates, leaving cross-activation structure unexploited. We show that matched CFG activations form a strongly correlated two-dimensional source and that, under a fixed bit budget, the choice of branch coding basis materially affects quantization fidelity. Motivated by this observation, we introduce $\text{branch-space transform coding}$, which rotates matched CFG branches via an offline derived $2\times 2$ orthogonal matrix, requiring minimal modifications to model parameters or the quantization pipeline. We further derive the $\text{Guidance-Correlation Branch Transform (GCBT)}$, which jointly incorporates the CFG guidance direction and cross-branch second moments. Under an equal-rate quantization-noise surrogate, GCBT admits a closed-form per-layer solution without gradient optimization or angle search. Applied on top of existing diffusion PTQ methods, GCBT yields statistically significant fidelity gains in most evaluated comparisons with no statistically significant degradation, while leaving the underlying host quantization pipeline unchanged.