Autoregressive models like WaveNet and WaveRNN, discussed previously, achieve high audio fidelity but suffer from a significant drawback: slow inference speed due to their sequential, sample-by-sample generation process. Generating even a few seconds of audio can take considerable time, making them challenging for real-time applications. Flow-based models offer an alternative approach that enables parallel waveform generation, drastically reducing synthesis time while maintaining high quality.
Flow-based models belong to the family of generative models known as Normalizing Flows. The fundamental idea is to learn an invertible mapping f between a simple base distribution pZ(z) (typically a standard Gaussian) and the complex target distribution pX(x) (the distribution of real audio waveforms). If we can sample z∼pZ(z) and compute x=f(z), we can generate realistic audio. Conversely, given an audio sample x, we can compute z=f−1(x) and evaluate its likelihood under the base distribution.
The transformation f is constructed as a sequence of simpler invertible functions f=fL∘⋯∘f2∘f1. For the model to be trainable via maximum likelihood, two conditions must be met:
The change of variables formula allows us to compute the exact log-likelihood of a data point x:
logpX(x)=logpZ(z)+logdet(∂x∂f−1(x))Equivalently, using the inverse function theorem:
logpX(x)=logpZ(f−1(x))−logdet(∂z∂f(z))z=f−1(x)Training involves maximizing this log-likelihood over the dataset.
WaveGlow is a prominent example of a flow-based neural vocoder, drawing inspiration from the Glow model originally developed for image generation. It directly maps a Gaussian distribution to speech waveforms, conditioned on mel-spectrograms.
Architecture: WaveGlow utilizes a single network architecture that performs both the forward (x→z) and inverse (z→x) transformations. Its core components are:
Overview of WaveGlow's transformation process during inference. Gaussian noise is passed through multiple steps of affine coupling layers and invertible 1x1 convolutions, conditioned on mel-spectrograms, to produce the output audio waveform. Each step is invertible, allowing for training via maximum likelihood.
Training and Inference: WaveGlow is trained by maximizing the log-likelihood of the ground truth audio waveforms given their corresponding mel-spectrograms. This involves passing the audio x through the forward transformation f−1 to get z=f−1(x∣mel), and then maximizing logpZ(z) plus the sum of the log-determinants from all layers.
Inference is highly parallel and efficient. You sample a random vector z from a standard Gaussian distribution, provide the conditional mel-spectrogram, and perform a single forward pass through the network x=f(z∣mel). Since the operations (convolutions, affine transformations) can be parallelized effectively on GPUs, synthesis is significantly faster than autoregressive models.
FloWaveNet is another flow-based vocoder architecture that shares similarities with WaveGlow but uses a different structure for its coupling layers, incorporating ideas from WaveNet's dilated causal convolutions within the affine coupling blocks. Like WaveGlow, it aims for fast, parallel waveform synthesis by learning an invertible transformation from noise to audio, conditioned on acoustic features.
Advantages:
Considerations:
Flow-based vocoders like WaveGlow represent a significant step forward in neural speech synthesis, striking an excellent balance between audio quality and inference speed. They are widely used in modern TTS systems where low latency is not the absolute primary constraint (unlike streaming ASR) but where faster-than-real-time synthesis is highly desirable. They provide a compelling alternative to both the slow generation of autoregressive models and the potentially less stable training of GAN-based vocoders.
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