Logical Guidance for the Exact Composition of Diffusion Models

Francesco Alesiani · Jonathan H. Warrell · Tanja Bien · Henrik Christiansen · Matheus Ferraz · Mathias Niepert

A logical rule, blue or amber and not a sphere, steers denoising through probability-aware guidance. Separate blue and amber cubes and cylinders illustrate different valid outcomes.

The method in a nutshell

“Blue or amber, but not a sphere” sounds simple. For a diffusion model, satisfying such rules takes more than averaging separate guidance signals.

LOGDIFF translates AND, OR, and NOT into a recursive guidance calculation. At each denoising step, it combines signals for individual properties using their probabilities given the current noisy sample.

This preserves multiple valid alternatives for OR and adapts the strength of NOT as unwanted properties become more or less likely.

Exact composition is guaranteed under the paper’s independence or exclusivity conditions, assuming exact input scores and probabilities.

The payoff: on Shapes3D queries with five AND/OR operators, LOGDIFF achieves 87.6% rule satisfaction, versus 57.9% for fixed-weight guidance. See Table 2.

Read the paper Code

Logical Guidance for the Exact Composition of Diffusion Models. ICML 2026. Publication record