We address the problem of encoding room impulse responses (RIRs) into high-order Ambisonics (HOA) representations from arbitrary and potentially insufficient or incomplete microphone array measurements. This task is fundamentally ill-posed for microphone arrays with limited spatial capture capabilities, such as irregular or sparse arrays, as classical linear methods fail to reconstruct high-order spatial detail. We introduce a diffusion-based generative framework that models the statistical properties of HOA RIRs. This enables device-agnostic encoding from arbitrary microphone arrays, potentially unseen during data measurement. Our approach incorporates a posterior sampling procedure that enforces consistency between the estimated signals and the measurements while plausibly reconstructing spatial information that is unobservable from the limited measurements alone. Experiments on simulated and measured data demonstrate that our method outperforms linear and neural baselines, achieving accurate HOA RIR estimation up to 12th order. A listening test with binaural renderings, including both simulated and measured RIRs, further confirms that the proposed method yields higher perceptual similarity to reference Ambisonics RIRs than all baselines. The flexibility and accuracy of the proposed framework open new possibilities for scalable acoustics simulations.