Trinity: One Differentiable Physics for Training, Refining and Scoring Generative Floorplanners

2026-10-04

AI Summary

This study addresses the inefficiency and opaque generative contributions of existing diffusion-based placers that rely on post-hoc corrections. We propose Trinity, a flow-matching-based placer that introduces six differentiable physical constraint functions spanning training, refinement, and scoring to enable end-to-end optimization. By internalizing physical rules within the network, Trinity eliminates the need for external guidance mechanisms during sampling. Integrating flow matching, differentiable physical modeling, closed-loop energy refinement, and a soft cost evaluation framework, the proposed method reduces raw soft cost by 26% and decreases refinement steps to between 1/16 and 1/660 of prior requirements. Furthermore, it achieves a 36% reduction in optimal soft cost and attains a hard cost of 1.014, demonstrating substantial improvements in both placement quality and computational efficiency.

Abstract

Floorplanning arranges the blocks of a chip and decides their shapes under objectives that press blocks together, short wirelength and a small outline, and constraints that hold them apart, non-overlap, clusters, MIB shapes and boundary blocks. Recent diffusion placers train on reference layouts alone and leave this coupled system to guidance, post-hoc loops and a legalizer, reporting only the endpoint, which hides what the generator contributes. We re-implement four of them under one recipe on FloorSet, score raw, refined and legalized layouts on one scale, and propose Trinity, a flow-matching floorplanner whose six differentiable functions for the constraints and objectives are its training loss term, the energy of a closed-form refiner after sampling and the base of a soft cost for every stage. The network thus learns the correction prior placers apply in their samplers, and sampling needs no guidance. Stage by stage, the training term lowers a plain transformer's raw soft cost by 26% and matters most at short budgets, the shared refiner decides more of the final cost than the generator and matches a ported placer's loop in 16 to 660 times fewer steps, Trinity's refined soft cost is 36% below the best ported pipeline, the soft cost ranks settings as the contest's hard cost does, and on the FloorSet val set the pipeline reaches a mean hard cost of 1.014 in 1.63 s per case.

Problem

• floorplanning
• diffusion models
• differentiable physics
• chip layout
• generative design

Innovation

• Differentiable Physics
• Flow Matching
• Floorplanning
• Closed-form Refiner
• Soft Cost