P-Guide: Parameter-Efficient Prior Steering for Single-Pass CFG Inference

Classifier-free guidance (CFG) improves conditional generation in Flow Matching, but strong guidance can distort the generated distribution and reduce diversity. We provide a geometric account of this behavior by viewing Flow Matching as a time-varying gradient flow and characterizing how CFG reshapes its underlying potential. This view explains how stronger alignment can be accompanied by mean displacement and trajectory concentration, and motivates controlling guidance through the model-implied terminal posterior mean. We therefore propose Posterior-Mean-Capped CFG (PMC-CFG), a training-free, per-sample method that adaptively retains the strongest feasible guidance without additional network evaluations. Experiments on synthetic and large-scale image-generation benchmarks show that PMC-CFG limits guidance-induced distortion and concentration while improving the alignment--diversity trade-off, with particularly strong benefits when nominal guidance is large.

Flow-based generative methods offer a simple and effective framework for high-fidelity generation, yet pretrained flow models are rarely used in their vanilla conditional form: in image generation, samples without guidance often appear diffuse and lack fine-grained detail. Existing guidance techniques such as classifier-free guidance (CFG) improve fidelity but reduce sample diversity. We introduce Momentum Guidance (MG), a guidance method that improves sample quality by extrapolating the current velocity away from an exponential moving average of past velocities along the ODE trajectory, while preserving the standard one-evaluation-per-step cost. MG provides gains beyond CFG, improving the precision-recall Pareto frontier. Experiments demonstrate the effectiveness of MG across benchmarks. On ImageNet-256, MG improves FID by 36.54% without CFG and 25.42% with CFG on average across sampling settings, attaining an FID of 1.553 at 16 sampling steps. Evaluations on large flow-based models, including Stable Diffusion 3 and FLUX.1-dev, further confirm improvements across standard metrics.

Classifier-free guidance (CFG) is the default mechanism for conditional generation in diffusion models, but the distribution sampled by its deterministic guided dynamics is not captured by the usual product-distribution heuristic $p_0^ωq_0^{1-ω}$. We analyze CFG through the probability flow ODE and derive exact analytic path-integral representations of the induced distributions for both constant and time-dependent guidance. The resulting formulas show that CFG modifies $p_{t_0}$ by an exponential path-integral correction, and that a time-dependent schedule enters this correction through the weight $ω(t)-1$. This characterization explains how score discrepancies accumulate along sampling trajectories and motivates Distribution-Guided CFG (DG-CFG), a schedule that balances timestep contributions while accounting for signal strength and low-noise score-error amplification. A toy model with analytic scores closely verifies the predicted distributions. Across Stable Diffusion1.5, Stable Diffusion2.1, and Stable DiffusionXL, DG-CFG yields a stronger diversity--fidelity trade-off and robustly mitigates the saturation and quality degradation caused by strong constant or heuristic guidance. Complete NFE experiments on Stable Diffusion1.5 and Stable Diffusion~2.1 confirm that these gains persist across sampling budgets, while fixed-quality experiments on both backbones show that DG-CFG reaches target metrics with fewer sampling steps.