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

Mingrun Jiang; Yuejia Liu; Zishan Shao; Ting Jiang; Qinsi Wang; Hancheng Ye; Yixiao Wang; Rui-Feng Wang

cs.CVOct 1, 2026

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

Authors: Mingrun Jiang, Yuejia Liu, Zishan Shao, Ting Jiang, Qinsi Wang, Hancheng Ye, Yixiao Wang, Rui-Feng Wang, +6 more

Organizations: Duke University · Carnegie Mellon University · University of Florida · Wake Forest University · University of Oxford

Abstract

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 branch-space transform coding, which rotates matched CFG branches via an offline derived 2x2 orthogonal matrix, requiring minimal modifications to model parameters or the quantization pipeline. We further derive the 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.

Figures & tables

Figure 1 : GCBT is a plug-and-play activation transform built on top of existing post-training quantizers in CFG-guided diffusion models. By applying a branch-wise rotation prior to quantization, it requires minimal modifications to model parameters or base pipelines. On PixArt- $\Sigma$ (top) and Sana-1.6B (bottom), GCBT demonstrates superior visual fidelity over naive PTQ and SVDQuant.

Figure 2 : Matched CFG branches are strongly correlated. Matched CFG branches exhibit substantially stronger cross-branch correlation than deliberately mismatched pairs.

Figure 3: Overview of branch-space coding. (a) Matched CFG activations define a two-dimensional branch axis at each token–feature coordinate. (b) Native quantizer $Q_{A}$ operates directly on $(X_{c},X_{u})$ , while branch-space coding rotates the pair, applies the same host quantizer in transformed coordinates, and rotates back. (c) The coding basis is determined jointly by the activation geometry $\Sigma_{\ell}$ and CFG branch direction $g_{s}$ , yielding the optimal coding axis $r_{1}^{\star}$ and angle $\theta_{\ell}^{\star}$ where $\theta_{\ell}^{\star}=\angle(X_{c},r_{1}^{\star})$ .

Data	Method	LPIPS $\downarrow$	SSIM $\uparrow$	PSNR $\uparrow$
MJHQ	CFG-Cal.	0.4775	0.5722	16.454
MJHQ	+GCBT	0.4634	0.5829	16.547
sDCI	CFG-Cal.	0.5310	0.4768	15.279
sDCI	+GCBT	0.5179	0.4872	15.352

Table 1 : GCBT after CFG-aware calibration. PixArt-

\Sigma

, W4A4, we implement ( Shafi and Suma, 2026 ) on SVDQuant given GAMP is closed-source. Bold: 95% CI excludes zero.

PTQ Hosts	Model	Method	MJHQ			sDCI
			LPIPS $\downarrow$	SSIM $\uparrow$	PSNR $\uparrow$	LPIPS $\downarrow$	SSIM $\uparrow$	PSNR $\uparrow$
SVDQuant W4A4	PixArt- $\Sigma$ CFG 4.5	Native	0.327	0.651	17.472	0.355	0.574	16.450
	PixArt- $\Sigma$ CFG 4.5	+ GCBT	0.296 $[0.024,0.038]$	0.695 $[0.039,0.050]$	17.917 $[0.287,0.607]$	0.319 $[0.029,0.043]$	0.625 $[0.047,0.057]$	17.017 $[0.418,0.708]$
	SANA-1.6B CFG 4.5	Native	0.230	0.702	17.283	0.234	0.651	16.565
	SANA-1.6B CFG 4.5	+ GCBT	0.210 $[0.015,0.026]$	0.730 $[0.023,0.033]$	17.825 $[0.383,0.703]$	0.213 $[0.016,0.025]$	0.685 $[0.029,0.038]$	17.051 $[0.364,0.608]$
Q-DiT W4A8	PixArt- $\Sigma$ CFG 4.5	Native	0.269	0.711	17.939	0.281	0.648	17.135

Table 2 : Quantitative evaluation of image-generation fidelity on MJHQ and sDCI (

n=256

). For each +GCBT row, the second line reports the pointwise paired 95% confidence interval of improvement (Native minus GCBT for LPIPS; GCBT minus Native for SSIM and PSNR). Bold denotes gains whose paired interval lies entirely above zero.

PTQ Host	Model	Method	Teacher Fidelity			VBench
			LPIPS $\downarrow$	SSIM $\uparrow$	PSNR $\uparrow$	S.C. $\uparrow$	A.Q. $\uparrow$	I.Q. $\uparrow$
OrbitQuant W4A4	Wan2.1-T2V-1.3B CFG 5	Native	0.545	0.497	12.871	0.957	0.527	0.672
	Wan2.1-T2V-1.3B CFG 5	+ GCBT	0.504	0.518	12.965	0.975	0.584	0.675
	CogVideoX-2B CFG 6	Native	0.427	0.639	17.474	0.927	0.494	0.593
	CogVideoX-2B CFG 6	+ GCBT	0.390	0.649	17.554	0.937	0.525	0.606
ViDiT-Q W4A8-MP	OpenSora v1.2 CFG 7	Native	0.544	0.540	13.871	0.935	0.455	0.490

Table 3 : Quantitative evaluation of video generation on VBench (

n=256

). Bold indicates statistically significant improvements (paired 95% CIs lie entirely in the favorable direction). Full paired confidence intervals are provided in Appendix Table 9 .

Figure 4 : Qualitative comparison of GCBT on image and video generation.

Basis	LPIPS $\downarrow$	SSIM $\uparrow$	PSNR $\uparrow$
Native	0.327	0.651	17.472
Guidance	0.315	0.678	17.707
GCBT	0.296	0.695	17.917

Table 4 : Branch-basis ablation. PixArt-

\Sigma

, SVDQuant W4A4 on MJHQ.

Figure 5 : Fidelity gains across CFG scales. GCBT achieves monotonically larger gains over native PTQ across all metrics as guidance scale

s

increases.

Figure 6 : System overhead comparison. Host+GCBT matches native engines in end-to-end latency and peak GPU memory across image and video pipelines, imposing minimal practical overhead.

$n_{\mathrm{geom}}$	Matched corr.	$\psi_{\ell}$	$\lambda_{1,\ell}/\lambda_{2,\ell}$
16	0.864	$42.89^{\circ}$	13.71
64	0.859	$42.71^{\circ}$	13.27
128	0.857	$42.67^{\circ}$	13.03

Table 5: Calibration stability. Layerwise medians.

Appendix figures & tables5 assets

Supplementary material from the paper’s appendix.

Appendix

$n_{\mathrm{geom}}$	Matched corr.	Mismatched corr.	$\psi_{\ell}$	$\lambda_{1,\ell}/\lambda_{2,\ell}$
16	0.8635	0.3166	$42.89^{\circ}$	13.71
32	0.8604	0.3243	$42.71^{\circ}$	13.46
64	0.8587	0.3276	$\mathbf{42.71^{\circ}}$	13.27
128	0.8569	0.3231	$42.67^{\circ}$	13.03

Appendix

Table 6 : Measurement-pool-size stability of CFG branch geometry on DiT-XL/2. Values are medians across 112 linear sites under repository-native SVDQuant W4A4 with an FP rank-32 branch. All sizes use nested class/noise inputs and frozen weights.

Dataset	LPIPS reduction $\uparrow$	$\Delta$ SSIM $\uparrow$	$\Delta$ PSNR (dB) $\uparrow$
MJHQ	$2.97\%\;[2.17,\,3.78]\%$	$+0.0107\;[0.0079,\,0.0135]$	$+0.093\;[-0.005,\,0.190]$
sDCI	$2.47\%\;[1.71,\,3.23]\%$	$+0.0104\;[0.0077,\,0.0132]$	$+0.073\;[-0.017,\,0.169]$

Appendix

Table 7 : Paired effects of GCBT after CFG-aware calibration. Positive values favor GCBT. LPIPS reports relative reduction, while SSIM and PSNR report absolute paired improvements. Brackets denote paired 95% confidence intervals.

(a) Absolute metrics: mean [95% CI]
Basis	LPIPS $\downarrow$	SSIM $\uparrow$	PSNR $\uparrow$
Native	$0.327\,[0.315,\,0.338]$	$0.651\,[0.638,\,0.664]$	$17.472\,[17.150,\,17.805]$
Guidance	$0.315\,[0.303,\,0.327]$	$0.678\,[0.664,\,0.691]$	$17.707\,[17.378,\,18.044]$
GCBT	$\mathbf{0.296}\,[0.284,\,0.308]$	$\mathbf{0.695}\,[0.682,\,0.708]$	$\mathbf{17.917}\,[17.584,\,18.256]$
(b) Paired improvements: mean [95% CI]
Candidate vs. reference	LPIPS reduction $\uparrow$	SSIM gain $\uparrow$	PSNR gain $\uparrow$

Appendix

Table 8 : Additional statistics for branch-basis ablation. Evaluated on PixArt-

\Sigma

(SVDQuant W4A4, CFG

s=4.5

) on MJHQ (

n=256

). Panel (a) reports absolute metric means with 95% CIs. Panel (b) reports paired improvements over the reference (positive values indicate improvement).

Figure 7 : Additional qualitative examples for the appendix. We show full-precision, native quantized, and GCBT outputs under the same prompts and generation settings.

Figure 8 : More Examples of GCBT Generation

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Closing the Null Space: Guidance-Aware Quantization for Classifier-Free Diffusion

Abdullah Al Shafi, Sumaiya Rahim Suma

Department of Computer Science and Engineering Khulna University of Engineering & Technology Khulna-9203, Bangladesh

Classifier-Free Guidance Post-Training Quantization Diffusion Models Degradation Closure

Open paper AskPDF arXiv

Deploying classifier-free guidance (CFG) diffusion models under real-world compute budgets requires quantization, yet existing post-training quantization (PTQ) methods treat CFG models as single-branch networks, ignoring the paired conditional/unconditional structure that CFG inference fundamentally relies on. This structural blind spot has two consequences. At the system level, the two-pass CFG execution pattern imposes a latency overhead that parameter-count and bit-operation metrics conceal entirely, and commodity INT8 inference stacks fail to realize the theoretical efficiency gains that BOPs calculations promise. At the algorithmic level, calibrating against the guidance gap alone admits an exact null space: a quantized model can achieve perfect gap-fidelity diagnostics while the unconditional branch drifts arbitrarily, corrupting every guided prediction at inference time. This paper terms this the branch-drift trap, proves its existence analytically, and confirms it empirically through a false-positive result in which the best-calibrated model by standard diagnostics simultaneously produces the worst sample quality. To close the trap, Guidance-Aware Mixed Precision (GAMP) is proposed, which calibrates directly on the guided prediction, derives per-layer activation-bit sensitivity from guided-output degradation, and allocates bits via a greedy knapsack -- provably preventing unconditional branch drift by construction.

Abstract

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