Summary: This work offers a statistical perspective on CFG in discrete diffusion:.• Explicit 1D/2D formulas.• Discussion of sampled distributions in terms of supports and local covariances.• Total variation bounds on convergence rates.Glad to discuss with anyone interested!.

TV distance to the generated distribution decays double-exponentially in guidance strength. • Strong guidance = faster convergence. But also more aggressive shifts = less numerical stability.

Guidance sharpens support around the target label and suppresses overlap. • 1-token: samples exactly from the tilted distribution, unlike continuous CFG.• Multi-token: differs from the tilted distribution.• We provide explicit formulas for the generated distributions.

In discrete diffusion, guidance isn’t just steering — it reshapes the distribution. We analyze:.• How CFG affects the sampled distributions.• How it changes how fast sampling converges.

New preprint: “What Exactly Does Guidance Do in Masked Discrete Diffusion Models” joint work with @KevRojas1499 @MoleiTaoMath. We provide a rigorous theoretical analysis of the sampling dynamics in masked discrete diffusion with classifier-free guidance.