From Generation to Discovery: Diffusion Mutation Kernels for Circuit and Physical Design

Generation and discovery are different problems. A generative model trained on valid artifacts reproduces a distribution, whereas discovery must produce artifacts that lie outside the observed corpus, satisfy hard structural constraints, and improve on established designs under evaluation that the model cannot influence. We introduce a diffusion-based discovery framework. Unlike conventional generative models that sample from learned distributions, it learns transition operators that transform existing artifacts into new candidates. Controlled partial re-noising followed by denoising defines a diffusion mutation kernel, a learned transition distribution that preserves the structural regularities of feasible designs while moving between regions of the design space. The learned model supplies feasibility structure only, and all correctness and performance judgments remain with external engineering tools. Intermediate diffusion trajectories are additionally monitored under a conformal risk budget so that unpromising candidates are discarded before expensive evaluation. We evaluate the framework on three electronic design spaces, an environment that supplies rigorous non-differentiable evaluators in the form of simulation, formal equivalence checking, and industrial physical implementation. The framework discovers 32-bit prefix adders that are formally verified equivalent to addition over all 2^64 input pairs and reduce delay by 17% and area by 18% relative to Kogge-Stone under a placed-and-timed flow; seven independently re-simulated amplifier topologies absent from the training corpus, spanning gains of 21.9-66.1 dB and bandwidths of 72.9 kHz-207 MHz; and macro placements on held-out netlists reaching 0.68x wirelength of an industrial placer.