MCLR: Improving Conditional Modeling via Inter-Class Likelihood-Ratio Maximization and Unifying Classifier-Free Guidance with Alignment Objectives

Classifier-Free Guidance (CFG) is a cornerstone of modern conditional diffusion models, yet its reliance on the fixed or heuristic dynamic guidance weight is predominantly empirical and overlooks the inherent dynamics of the diffusion process. In this paper, we provide a rigorous theoretical analysis of the Classifier-Free Guidance. Specifically, we establish strict upper bounds on the score discrepancy between conditional and unconditional distributions at different timesteps based on the diffusion process. This finding explains the limitations of fixed-weight strategies and establishes a principled foundation for time-dependent guidance. Motivated by this insight, we introduce \textbf{Control Classifier-Free Guidance (C$^2$FG)}, a novel, training-free, and plug-in method that aligns the guidance strength with the diffusion dynamics via an exponential decay control function. Extensive experiments demonstrate that C$^2$FG is effective and broadly applicable across diverse generative tasks, while also exhibiting orthogonality to existing strategies.

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.

Diffusion models generate samples by learning to reverse a fixed corruption process, and classifier-free guidance (CFG) is the standard mechanism for conditioning this process on a desired class or prompt. CFG can be applied at varying guidance strengths, and while higher strengths improve image quality and conditional alignment, too high a guidance strength can degrade image quality and diversity. Furthermore, CFG violates principled diffusion sampling dynamics, and existing explanations for why it works despite the violation disagree on the underlying theory or do not extend to deterministic samplers used in practice. We address both these issues. We first frame CFG sampling as a continuous-time optimal control problem, treating the sampling trajectory as a sequence of controls chosen to maximise the probability of the desired condition. Solving the resulting Hamilton--Jacobi--Bellman equation shows that CFG is recovered under specific path costs when using an unconstrained control set. We argue this lack of constraint is responsible for CFG's failure at high guidance strengths, since it permits the sampling path to move arbitrarily far from the current image estimate. To fix this, we propose curvature-aware CFG (CACFG), which constrains the control set to a hypersphere informed by the Gaussian regularisation used when training variational autoencoders. We show that the control inputs produced by CFG sampling routinely violate this bound, and that across diffusion models, datasets, and guidance schedules, CACFG achieves superior generative quality at mid-to-high guidance strengths with a less severe quality-diversity tradeoff than regular CFG.