Probability-Conserving Flow Guidance

2026-05-19

AI Summary

This work addresses the issue that existing guidance methods, such as Classifier-Free Guidance, violate probability conservation under strong guidance, causing generated samples to deviate from the data manifold and resulting in distortion or hallucination. By formulating guidance through the continuity equation, the authors decompose its effect into a divergence term and a score-parallel term, revealing the correspondence between prevailing heuristics and theoretically grounded components. They propose AdaMaG, a plug-in adaptive guidance strategy that incurs no additional inference cost and employs a time-dependent scheduling mechanism to dynamically balance the contributions of these two terms. This approach preserves manifold structure while enabling high-fidelity generation. Experiments demonstrate that AdaMaG significantly enhances realism, suppresses hallucination on image generation benchmarks, and achieves controllable desaturation under high guidance strengths, outperforming current state-of-the-art methods.

Abstract

Diffusion and flow-based generative models dominate visual synthesis, with guidance aligning samples to user input and improving perceptual quality. However, Classifier-Free Guidance (CFG) and extrapolation-based methods are heuristic linear combinations of velocities/scores that ignore the generative manifold geometry, breaking probability conservation and driving samples off the learned manifold under strong guidance. We analyse guidance through the continuity equation and show its effect decomposes into a divergence term and a score-parallel term defined invariantly across parameterisations. We prove the divergence term blows up structurally as sampling approaches the data manifold, motivating a time-dependent schedule alongside score-parallel attenuation. The resulting plug-and-play rule, Adaptive Manifold Guidance (AdaMaG), bounds both terms at no additional inference cost. Finally, we show that most empirical heuristics for reducing saturation or improving generation quality correspond directly to the two terms in our decomposition. Across image generation benchmarks, AdaMaG improves realism, reduces hallucinations, and induces controlled desaturation in high-guidance regimes.

Problem

• probability conservation
• generative manifold
• guidance
• flow-based models
• diffusion models

Innovation

• Probability Conservation
• Flow Guidance
• Generative Manifold
• Continuity Equation
• Adaptive Manifold Guidance