Generative adversarial distillation (GAD) provides on-policy feedback for black-box distillation by training a discriminator that ranks teacher and student responses to the same prompt. While effective, GAD is also costly: every step pays for a discriminator update, an actor update over the full response, and the indirect cost of recovering whenever the discriminator and the actor progress at incompatible rates. We argue that the right way to make GAD efficient is not to make individual updates cheaper but to decide **when each update is worth its cost**. We introduce **curriculum-efficient GAD (CE-GAD)**, an adaptive recipe that monitors a small set of training signals and uses them to:

- (i) skip discriminator updates that would not change the reward, - (ii) constrain actor updates and prune per-token gradients to the subset that actually carries signal, and - (iii) rescale rewards and normalize advantages to preserve within-batch contrast under saturation.

Evaluations across four models from two open-source families (Qwen2.5 at 3B/7B/14B and Llama-3.2-3B) demonstrate that CE-GAD matches or surpasses vanilla GAD on quality while winning on 12 out of 16 individual benchmark configurations. Specifically, on Qwen2.5-7B, CE-GAD improves the average score by up to **+3%** relative compared to the base model, while reducing per-step wall-clock time by up to **8x** relative to vanilla GAD.

In settings where labeled verifiable training data is the binding constraint, each checked example should be allocated to the model and reward density where it is most informative. We identify a reward-density principle: sparse sequence-level reward is most useful on models that can explore and discover better behavior, while dense token-level teacher supervision is better suited for compressing that behavior into a smaller deployment model; accordingly, scarce labeled data should be used upstream on the strongest available teacher, then transferred downstream as dense supervision.

We evaluate this rule through a four-stage workflow: teacher RL, forward-KL warmup, on-policy distillation, optional post-bridge student RL on verifiable math and code generation with Qwen3, Llama, and Qwen2.5 models. At fixed Qwen3-1.7B deployment-student size, an RL-improved 8B teacher distilled through the dense bridge outperforms direct GRPO on the same student (79.3% vs. 75.9% on MATH; 25.2% vs. 19.8% on AIME2024, avg@16), while transfer from the same teacher before RL underperforms. A component ablation confirms that each stage is load-bearing: the RL-improved teacher adds 7.8 absolute points on MATH over a raw teacher of the same size, the forward-KL warmup adds 1.7, and on-policy distillation adds 3.3. The teacher-quality ordering: raw-teacher transfer < direct GRPO < RL-teacher transfer replicates on Llama-3.1-8B-Instruct with a Llama-3.3-70B-Instruct teacher and on Qwen2.5-7B-Instruct for code generation with a Qwen2.5-32B-Instruct teacher, where the dense bridge improves HumanEval and MBPP by 3.3 and 3.8 absolute points, respectively, over direct student GRPO. The operational lesson is to avoid spending scarce labeled data on the least prepared policy: use sparse reward for teacher-side discovery, dense transfer for student compression, and student-side sparse reward only after the bridge. The OPD implementation used in our experiments is available at https://github.com/HJSang/OPSD_OnPolicyDistillation.