Opening the Black Box of Classifier-Free Guidance via Information Bottleneck

Jiayang Gao; Tianyi Zheng; Jiayang Zou; Fengxiang Yang; Luyao Fan; Lv Tang; Bo Li; Jia Wang

cs.LGOct 9, 2026

Opening the Black Box of Classifier-Free Guidance via Information Bottleneck

Authors: Jiayang Gao, Tianyi Zheng, Jiayang Zou, Fengxiang Yang, Luyao Fan, Lv Tang, Bo Li, Jia Wang

Organizations: Shanghai Jiao Tong University, Shanghai, China · vivo BlueImage Lab, vivo Mobile Communication Co., Ltd., China · Stanford University, California, USA · Michael Smith Laboratories, University of British Columbia

Abstract

Classifier-free guidance (CFG) is a standard technique for improving conditional generation in diffusion models, yet its activation schedule is usually selected heuristically. In practice, most existing CFG-based methods rely on a pre-defined activation policy throughout inference, while recent dynamic variants often depend on hand-designed schedules without a principled theoretical explanation of when conditional information is most useful. In order to understand how the informational relevance between conditioning inputs and the score function evolves over the course of generation, we explore when guidance should be activated from an information-theoretic perspective. In this work, we formulate the diffusion trajectory as a time-dependent information bottleneck and show that the effectiveness of conditional information is not uniform throughout sampling, but becomes significantly stronger after a critical stage characterized by a Fisher-information balance condition. Motivated by this insight, we propose a training-free dynamic CFG strategy for inference. Rather than prescribing a fixed schedule in advance, our method constructs a stochastic process from conditional and unconditional score statistics and activates guidance when the estimated guidance gain crosses a prescribed threshold. This yields an adaptive activation rule that aligns condition injection with the underlying generation dynamics, while also recovering interval-based guidance as a limiting special case. Extensive experiments across diverse architectures and tasks, demonstrate that our method is effective, robust, and broadly applicable. Beyond empirical improvements, our framework provides an interpretation of dynamic guidance methods and a principled foundation for inference-time control in conditional diffusion models.

Figures & tables

Figure 1: Sensitivity of the solution $t^{*}$ to the hyperparameter in the original and simplified formulations. The original parameterization ( red $\Delta t$ ) exhibits a much flatter $\log\beta$ – $t$ relationship than the rescaled version ( blue $\Delta t$ ), indicating higher sensitivity to perturbations. Notably, for a fixed perturbation in $\log\beta$ , the resulting deviation in $t$ ( $\Delta t$ ) is significantly larger in the original formulation. Experiments are conducted on SiT-XL/2.

Figure 2: Overview of our adaptive CFG activation pipeline. Starting from noise, the diffusion model jointly evaluates conditional and unconditional scores at each reverse step, computes a guidance-gain statistic $\Delta\mathcal{J}(t)$ , and activates classifier-free guidance only after the stopping criterion is met. The illustration uses a DiT/SiT-style diffusion backbone.

Table 3

Model	Approach	FID $\downarrow$	HPS v2.1					CLIP $\uparrow$	Aesthetic $\uparrow$
Model	Approach	FID $\downarrow$	paintings $\uparrow$	photo $\uparrow$	concept-art $\uparrow$	anime $\uparrow$	average $\uparrow$	CLIP $\uparrow$	Aesthetic $\uparrow$
SD 3 (1024, 28 steps)	CFG( $\omega=7.5,B=4$ )	25.98	30.99	28.39	30.63	31.31	30.33	31.83	5.44
SD 3 (1024, 28 steps)	Interval( $\omega=7.5,\ t_{h}=0.7T$ )	–	27.66	24.76	27.57	28.55	27.13	31.41	5.21
	Ours( $\omega=7.5,\ \log\beta^{*}=10.0$ )	24.88	31.12	28.57	30.98	31.51	30.55	31.89	5.45
FLUX.1 (256, 50 steps)	CFG( $\omega=1.5,B=64$ )	30.93	29.77	27.18	29.21	30.80	29.24	31.10	5.46
FLUX.1 (256, 50 steps)	Ours( $\omega=1.5,\ \log\beta^{*}=8.0$ )	30.36	29.87	27.38	29.26	30.94	29.36	30.93	5.48

Table 3: Quantitative comparison on text-to-image tasks. Quantitative results on SD3 and FLUX.1 under different guidance configurations. We report FID, HPSv2.1, CLIP Score, and Aesthetic Score where available. For FLUX.1 at

1024\times 1024

, we additionally evaluate single-sample inference (

B=1

). “–” denotes unavailable results.

Table 5

Figure 3: Qualitative Comparison. Visual results on text-to-image tasks using Stable Diffusion 3 and Flux.1. The red text in the prompts highlights specific details that the baseline fails to generate.

Appendix figures & tables5 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 4: Probability density function (PDF) of the stopping time

\tau

. The histogram represents the empirical distribution of sampled

\tau

values. The solid curve is the fitted Weibull PDF, and the dashed curve is the Kernel Density Estimation (KDE) curve.

ImageNet $B=48$
Model-256, 50k samples, 250 inference timesteps	FID $\downarrow$	IS $\uparrow$	sFID $\downarrow$
SiT-XL/2 (REPA)( $\omega=1.35$ , SDE)	1.80	284.0	4.5
SiT-XL/2 (REPA, Interval) ( $\omega=1.8,t_{l}=0,t_{h}=0.7$ )	1.42	305.7	4.7
SiT-XL/2 (REPA) ( $\omega=1.8,t_{l}=0,t_{h}=0.68$ )	1.43	299.3	4.7
SiT-XL/2 (REPA) ( $\omega=1.9,t_{l}=0,t_{h}=0.68$ )	1.42	310.4	4.7
SiT-XL/2 (REPA) + Ours ( $\omega=1.9,\log\beta^{*}=5.9$ )	1.41	306.6	4.7

Appendix

Table 7: Comparison of fixed and stochastic stopping strategies on ImageNet 256. We evaluate a deterministic variant that uses the empirical mean stopping time (

t_{h}=\bar{\tau}\approx 0.68

) against Interval Guidance and our proposed stochastic stopping method. While the mean-based threshold improves over the baseline, it remains inferior to the stochastic strategy, highlighting the importance of modeling the variability of stopping time.

ImageNet( 256 $\times$ 256 ), 10k samples, 50 inference timesteps
SiT-XL/2 (REPA), SDE	FID $\downarrow$	IS $\uparrow$
Baseline( $\omega=1.8,t_{h}=0.7,t_{l}=0,B=32$ )	5.09	287. 4
Ours( $\omega=1.9,\log\beta^{*}=5.5$ )	5.27	282.3
Ours( $\omega=1.9,\log\beta^{*}=5.7$ )	5.07	291.1
Ours( $\omega=1.9,\log\beta^{*}=5.9$ )	4.92	299.7
Ours( $\omega=1.9,\log\beta^{*}=6.1$ )	4.85	307.5

Appendix

Table 8: Ablation comparison on

\log\beta^{*}

. Comparison of different evaluation metrics on Class-Conditional ImageNet datasets with different

\log\beta^{*}

Figure 5: FID-IS trajectory under varying

\log\beta^{*}

based on Table 8 . Each point corresponds to a specific

\log\beta^{*}

value along the trajectory. As

\log\beta^{*}

increases, IS improves while FID exhibits a U-shaped trend, reflecting the quality-diversity trade-off in generation.

Panel of Figure 6 — Figure 6: Additional visual results on different models.

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Information-Theoretic Classifier-Free Guidance with Adaptive Schedule Optimization

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Diffusion Model Guidance Classifier-Free Guidance Diffusion-Based Image Generation

Open paper AskPDF arXiv

Diffusion models have achieved strong performance in image, text-to-image, and video generation, where conditional generation is often controlled by classifier-free guidance (CFG). CFG improves condition consistency by increasing a guidance weight, but stronger guidance typically reduces diversity and distributional coverage. It remains unclear how this consistency-coverage trade-off should be controlled across the reverse trajectory, since the distribution induced by CFG is not simply the fixed-time tilted distribution given by the guided score field. To address this issue, we propose an information-theoretic framework for CFG schedule optimization. Our approach uses a clean endpoint reference to specify the desired consistency-coverage trade-off, while optimizing the actual distribution induced by the guided sampler toward this reference. We derive trajectory-level formulas to estimate the objective from samples and score evaluations, avoiding explicit density estimation. On ImageNet-512 with EDM-XXL and COCO with SD-XL, the learned schedules achieve competitive or improved trade-offs over constant guidance and allocate guidance selectively across noise levels.

Abstract

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