Steering code generation toward working programs with constraints

Code generation via discrete diffusion iteratively refines token sequences, exposing intermediate program states where constraints can be enforced. This paper introduces Constrained Diffusion for Code (CDC), a training-free framework that integrates constraint satisfaction into the denoising process using mathematical optimization and program analysis. CDC identifies constraint-relevant regions in intermediate programs and locally adjusts the generation trajectory to steer toward feasible outputs. On code generation benchmarks, CDC improves constraint satisfaction across functional correctness, security, and syntax metrics, outperforming both discrete diffusion and autoregressive baselines with fewer corrective edits.