# LP-CFM: Perceptual Invariance-Aware Conditional Flow Matching for Speech Modeling

arXiv: https://arxiv.org/abs/2512.20314 · HTML: https://mlsanity.com/paper/2512.20314/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Audio, speech and music, one of 14 directions in Diffusion models.
- Builds on 20 of its 24 references that are in the map.
- First posted on arXiv 23 Dec 2025.

## Placed in

- Diffusion models / [Audio, speech and music](https://mlsanity.com/diffusion/audio-speech-and-music/)

## Builds on (most cited first, 20 of 20)

- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [HiFi-GAN: Generative Adversarial Networks for Efficient and High Fidelity Speech Synthesis](https://mlsanity.com/paper/2010.05646/) (2020)
- [ConvNeXt V2: Co-designing and Scaling ConvNets with Masked Autoencoders](https://mlsanity.com/paper/2301.00808/) (2023)
- [SDR - half-baked or well done?](https://mlsanity.com/paper/1811.02508/) (2018)
- [Conv-TasNet: Surpassing Ideal Time-Frequency Magnitude Masking for Speech Separation](https://mlsanity.com/paper/1809.07454/) (2018)
- [UTMOS: UTokyo-SaruLab System for VoiceMOS Challenge 2022](https://mlsanity.com/paper/2204.02152/) (2022)
- [Parallel WaveGAN: A fast waveform generation model based on generative adversarial networks with multi-resolution spectrogram](https://mlsanity.com/paper/1910.11480/) (2019)
- [Attention is All You Need in Speech Separation](https://mlsanity.com/paper/2010.13154/) (2020)
- [Matcha-TTS: A fast TTS architecture with conditional flow matching](https://mlsanity.com/paper/2309.03199/) (2023)
- [TasNet: time-domain audio separation network for real-time, single-channel speech separation](https://mlsanity.com/paper/1711.00541/) (2017)
- [Generative Pre-training for Speech with Flow Matching](https://mlsanity.com/paper/2310.16338/) (2023)
- [MossFormer2: Combining Transformer and RNN-Free Recurrent Network for Enhanced Time-Domain Monaural Speech Separation](https://mlsanity.com/paper/2312.11825/) (2023)
- [Chunked Autoregressive GAN for Conditional Waveform Synthesis](https://mlsanity.com/paper/2110.10139/) (2021)
- [MossFormer: Pushing the Performance Limit of Monaural Speech Separation using Gated Single-Head Transformer with Convolution-Augmented Joint Self-Attentions](https://mlsanity.com/paper/2302.11824/) (2023)
- [Faces that Speak: Jointly Synthesising Talking Face and Speech from Text](https://mlsanity.com/paper/2405.10272/) (2024)
- [FlowSE: Flow Matching-based Speech Enhancement](https://mlsanity.com/paper/2508.06840/) (2025)
- [PeriodWave: Multi-Period Flow Matching for High-Fidelity Waveform Generation](https://mlsanity.com/paper/2408.07547/) (2024)
- [WaveFM: A High-Fidelity and Efficient Vocoder Based on Flow Matching](https://mlsanity.com/paper/2503.16689/) (2025)
- [Unrestricted Global Phase Bias-Aware Single-channel Speech Enhancement with Conformer-based Metric GAN](https://mlsanity.com/paper/2402.08252/) (2024)
- [EDNet: A Versatile Speech Enhancement Framework with Gating Mamba Mechanism and Phase Shift-Invariant Training](https://mlsanity.com/paper/2506.16231/) (2025)

## Abstract (arXiv)

The goal of this paper is to provide a new perspective on speech modeling by incorporating perceptual invariances such as amplitude scaling and temporal shifts. Conventional generative formulations often treat each dataset sample as a fixed representative of the target distribution. From a generative standpoint, however, such samples are only one among many perceptually equivalent variants within the true speech distribution. To address this, we propose Linear Projection Conditional Flow Matching (LP-CFM), which models targets as projection-aligned elongated Gaussians along perceptually equivalent variants. We further introduce Vector Calibrated Sampling (VCS) to keep the sampling process aligned with the line-projection path. In neural vocoding experiments across model sizes, data scales, and sampling steps, the proposed approach consistently improves over the conventional optimal transport CFM, with particularly strong gains in low-resource and few-step scenarios. These results highlight the potential of LP-CFM and VCS to provide more robust and perceptually grounded generative modeling of speech.