arXiv:2605.23954v4 Announce Type: replace-cross Abstract: Large Audio Language Models (LALMs) remain vulnerable to acoustic noise, which can obscure task-relevant evidence and produce unreliable responses. We propose EchoDistill, a noisy-to-clean self-distillation framework that uses clean audio as privileged information during post-training. A noisy-input student samples candidate responses reflecting its inference-time behavior, while a frozen copy of the same backbone processes the corresponding clean audio. EchoDistill combines masked response-token distillation, task-gated consistency shaping, and teacher-referenced group-relative optimization to align noisy-input generation with clean-conditioned semantics. Only the student is retained at inference time, introducing no additional inference cost. Across three LALM backbones and three audio domains at -10dB, EchoDistill improves average noisy-input accuracy by 1.63 percentage points over the strongest baseline. On Qwen2.5-Omni, it raises noisy-input accuracy from 59.33% to 62.94%, while clean-audio accuracy increases from 76.56% to 77.56%. Replacing matched audio with random, shuffled, or silent inputs reduces accuracy by 3.08-6.42 points, confirming that matched acoustic evidence contributes to its predictions. Additional evaluations show improvements on held-out additive noises and external benchmarks, while revealing that these gains do not reliably extend to non-additive distortions. These results demonstrate robust post-training improvements under severe additive noise without sacrificing clean-audio capability across diverse tasks.