# RIPPLE: Generating Multi-Channel Phase, Not Recovering It

arXiv: https://arxiv.org/abs/2607.27775 · HTML: https://mlsanity.com/paper/2607.27775/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 30 references that are in the map.
- First posted on arXiv 30 Jul 2026.

## Builds on (most cited first, 14 of 14)

- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [High-Fidelity Audio Compression with Improved RVQGAN](https://mlsanity.com/paper/2306.06546/) (2023)
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- [One Transformer Fits All Distributions in Multi-Modal Diffusion at Scale](https://mlsanity.com/paper/2303.06555/) (2023)
- [Vocos: Closing the gap between time-domain and Fourier-based neural vocoders for high-quality audio synthesis](https://mlsanity.com/paper/2306.00814/) (2023)
- [Riemannian Continuous Normalizing Flows](https://mlsanity.com/paper/2006.10605/) (2020)
- [BinauralGrad: A Two-Stage Conditional Diffusion Probabilistic Model for Binaural Audio Synthesis](https://mlsanity.com/paper/2205.14807/) (2022)
- [LAFMA: A Latent Flow Matching Model for Text-to-Audio Generation](https://mlsanity.com/paper/2406.08203/) (2024)
- [OmniAudio: Generating Spatial Audio from 360-Degree Video](https://mlsanity.com/paper/2504.14906/) (2025)
- [Spatial LibriSpeech: An Augmented Dataset for Spatial Audio Learning](https://mlsanity.com/paper/2308.09514/) (2023)
- [BinauralFlow: A Causal and Streamable Approach for High-Quality Binaural Speech Synthesis with Flow Matching Models](https://mlsanity.com/paper/2505.22865/) (2025)
- [High Resolution Seismic Waveform Generation using Denoising Diffusion](https://mlsanity.com/paper/2410.19343/) (2024)
- [Broadband Ground Motion Synthesis by Diffusion Model with Minimal Condition](https://mlsanity.com/paper/2412.17333/) (2024)
- [FOA Tokenizer: Low-bitrate Neural Codec for First Order Ambisonics with Spatial Consistency Loss](https://mlsanity.com/paper/2510.22241/) (2025)

## Abstract (arXiv)

Generative models synthesize magnitude spectra with high fidelity, while phase is delegated to a recovery module---Griffin--Lim, a vocoder, or a latent decoder---applied independently to each channel. For multi-channel waveforms this delegation is costly: the physical content of spatial audio and three-component seismograms lives in the phase relationships between channels, precisely what channel-independent recovery cannot produce. The cost is also invisible, since the magnitude-based metrics common to both fields barely move when inter-channel phase coherence collapses---so a pipeline can discard the physical information in its output while still scoring well. We argue that phase should be generated, not recovered, and present RIPPLE (Rectified Inter-channel Phase with Prior-based LEarning), which reinterprets Griffin--Lim as a phase **prior** rather than a final estimator: initialized from the source phase, this prior carries the inter-channel structure to be preserved, and a rectified flow refines it toward the target under an explicit inter-channel phase loss. Tested on first-order ambisonics environment transfer and seismic cross-station translation---two physically unrelated domains---RIPPLE outperforms recovery-based pipelines on the coherence metrics that downstream analyses consume. The seismic case is decisive: across architecturally distinct generators, per-channel recovery leaves S-wave polarization error near the 57.3^circ random expectation, whereas learned phase reduces it to 33.8^circ.