Analytic Distribution of Classifier-Free Guidance for Schedule Design

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.

Classifier-free guidance (CFG) is the standard way to strengthen class-conditioning in diffusion and flow-matching samplers, yet at large guidance it oversaturates and destabilizes, symptoms practitioners suppress with more steps or limited-interval schedules. We analyze CFG through an asymptotic-preserving, numerical-analysis lens. Building on a recent result that the deterministic DDIM step is the unique fitted operator for the unguided terminal layer, exact on the final small-sigma stretch of sampling, we show that guidance re-stiffens exactly the discriminative subspace to an anomalous exponent 1+w. DDIM is therefore no longer fitted there, and on coarse meshes its guided residual diverges as sigma_min goes to zero. We prove a guided clock barrier with three ordered step-size thresholds, and read one-step oversaturation as its endpoint: a solver artifact on the calibration model rather than the continuous guided law. The same analysis yields a one-coefficient, zero-extra-NFE repair: replace CFG's w(r-1) by r^(1+w)-r on the guidance direction. On the calibration model's discriminative crossover, this removes CFG's sigma_min-divergent blow-up and is first-order accurate against the exact guided flow as sigma_min goes to zero. On learned CIFAR-10 checkpoints, and as a cross-domain smoke test on Stable Diffusion 1.5 DDIM, it acts as a high-guidance stabilizer at no extra cost rather than a universal quality knob: it cuts residual amplification and saturation, gives 9/9 point-FID wins over CFG on the tested grid, and preserves classifier-proxy target accuracy in the hard-cell blocks. We report the limits alongside: it is not a universal image-quality win, and against a dense vanilla-CFG reference it is not a uniformly better integrator of that field.

As Classifier-Free Guidance (CFG) has proven effective in conditional diffusion model sampling for improved condition alignment, many applications use a negated CFG term as a Negative Prompting (NP) to filter out unwanted features from samples. However, simply negating CFG guidance creates an inverted probability distribution, often distorting samples away from the marginal distribution. Inspired by recent advances in conditional diffusion models for inverse problems, here we present a novel method to achieve guidance toward the given condition using contrastive loss. Specifically, our guidance term aligns or repels the denoising direction based on the given condition through contrastive loss, achieving a similar guiding effect to traditional CFG for positive conditions while overcoming the limitations of existing negative guidance methods. Experimental results demonstrate that our approach effectively injects or removes the given concepts while maintaining sample quality across diverse scenarios, from simple class conditions to complex and overlapping text prompts.