Array-Agnostic Ambisonics Encoding via Diffusion Posterior Sampling

Technical Summary: Ambisonics Diffusion Encoding via Posterior Sampling (ADEPS)

Problem Statement
Spatial audio relies on Ambisonics to represent 3D sound fields, a format theoretically independent of recording configurations. However, practical implementation requires extracting Ambisonics coefficients from physical microphone arrays, a process constrained by hardware-specific limitations. These limitations introduce severe encoding artifacts, including noise amplification at low frequencies, non-uniform sensitivity due to irregular microphone positioning, and high-frequency spatial aliasing when sensor counts are insufficient.

Existing solutions face a trade-off: classical model-based methods (e.g., linear inversion) suffer from ill-conditioning and noise amplification, while data-driven neural approaches are typically restricted to fixed array geometries. Adapting these neural networks to new microphone counts or layouts requires complete retraining, and they often fail to generalize across arbitrary topologies. The core challenge addressed is achieving array-agnostic encoding that compensates for specific array distortions without requiring retraining for every new configuration.

Methodology: ADEPS
The authors propose Ambisonics Diffusion Encoding via Posterior Sampling (ADEPS), a generative framework that integrates the physical signal acquisition model directly into the inference process. The methodology operates as follows:

1. Generative Prior: An unsupervised diffusion model is trained exclusively on ideal, uncorrupted Ambisonics coefficients (the target distribution). Crucially, this training data is independent of any specific microphone array geometry, ensuring the learned prior is agnostic to hardware artifacts.
2. Physical Signal Model: The framework explicitly models the forward degradation process. This includes the physical spatial sampling of the sound field by the specific microphone array, the associated Array Transfer Functions (ATFs), and the linear encoding step.
3. Diffusion Posterior Sampling (DPS): During inference, ADEPS treats encoding as an inverse problem. It samples from the posterior distribution of ideal Ambisonics coefficients conditioned on the observed, degraded microphone signals.
   • The process utilizes a score-based generative model where the score function is decomposed into an unconditional prior (the learned ideal Ambisonics distribution) and a conditional likelihood term.
   • The likelihood term enforces measurement consistency by minimizing the error between the observed signals and the signals reconstructed from the current estimate of the Ambisonics coefficients, using the known physical degradation model.
4. Inference Pipeline: The system operates in the Short-Time Fourier Transform (STFT) domain with a magnitude-compression operator to handle the heavy-tailed distribution of speech. It iteratively refines the estimate by solving an Ordinary Differential Equation (ODE) that balances the generative prior with the physical constraints of the specific array being used.

Key Contributions

• Array-Agnostic Framework: ADEPS enables zero-shot encoding across arbitrary microphone array topologies and channel counts. Because the generative prior is trained only on ideal Ambisonics, the model does not need to be retrained when the microphone configuration changes.
• Explicit Physical Modeling: Unlike purely data-driven black-box approaches, ADEPS embeds the physical acquisition model (steering matrices, radial functions) into the inference loop, allowing it to explicitly invert array-specific distortions.
• Superior Performance in Reverberant Environments: The method addresses challenges inherent to Ambisonics encoding, such as noise amplification (C1), non-uniform sensitivity (C2), and spatial aliasing (C3), by leveraging the learned prior to guide the reconstruction.

Experimental Results
The authors evaluated ADEPS on diverse simulated and real microphone arrays, including irregular configurations with 4, 5, and 6 microphones, as well as the Project Aria array. The evaluation compared ADEPS against traditional linear encoding (Tikhonov-regularized pseudo-inverse) and parametric synthesis methods.

• Ideal Scenario (Order Match): In scenarios where the effective Ambisonics order matched the prior order, ADEPS consistently outperformed baselines across all metrics, achieving significantly higher Signal-to-Interference Ratio (SISDR), lower spectral error, and reduced Interaural Level Difference (ILD) and Interaural Coherence (IC) errors.
• Mismatch Scenario (Order Mismatch): Even when the prior order was lower than the effective spatial order of the array (a mismatch scenario), ADEPS maintained a clear lead in SISDR and spectral fidelity over linear and parametric baselines, though coherence metrics showed some degradation due to unmodeled high-frequency spatial folding.
• Comparison with Array-Specific Networks: When compared to a U-Net encoder trained specifically on a 4-microphone array, ADEPS achieved comparable or superior performance in most metrics despite being trained without exposure to that specific array geometry (zero-shot capability).

Significance and Claims
The paper claims that ADEPS represents a significant advancement in spatial audio acquisition by decoupling the encoding process from specific hardware constraints. By formulating the problem as a diffusion posterior sampling task, the method effectively compensates for array-specific distortions while maintaining flexibility across arbitrary topologies. The authors note that while the current framework is restricted to spatially resolvable orders, it successfully demonstrates that a generative prior trained on ideal data can be used to invert physical degradation models in a zero-shot manner, outperforming both traditional linear methods and existing data-driven approaches that lack channel flexibility.