The Verifier is the Curriculum: Execution-Gated Self-Distillation for Cross-Family Game Generation

Abstract

Post-training a code generator against a learned judge can optimize proxy features that raise the score without improving the artifact. We study the opposite signal: a deterministic, judge-free, ungameable filter -- whether a generated project launches cleanly under a headless engine (strict-launch). Under this gate, rejection-sampling self-distillation compounds out-of-family generalization. On GameCraft-Bench (mapping a natural-language brief to a complete Godot project), a 14B model (Qwen3-14B+LoRA) distilled under strict-launch raises clean generation on four unseen game families from 8.8% to 42.2% per-candidate and best-of-K coverage from 18/25 to 25/25 (the gold ceiling) over three rounds, each a significant gain (p=0.0019, p<1e-4, p<1e-4). The gain is not from merely adding data: an exactly-matched gold-duplication control regresses below the base model (5.6% vs. 8.8%, p=0.019), while a count-matched decomposition splits the round-1-to-2 jump into comparable quality (+8.8pp) and quantity (+8.5pp) channels. Most directly, rerunning the loop with only the filter swapped -- the lenient BUILD check, which passes 99.9% of generations, in place of the launch gate -- erases the gain entirely (back to base, p=1e-3 vs. the launch-gated round), isolating verifier precision rather than the optimizer. A second ungameable signal, headless execution grounding, rises monotonically across rounds and yields far more grounded candidates than gold-duplication at a matched budget (16 vs. 5), confirming the gains are functional, not launch-but-empty. Game generation is a verifiable testbed for one lesson: the verifier is the curriculum -- what it certifies is what the model learns.