Energy-Based Models For Speech Synthesis

Noise contrastive estimation (NCE) is a popular method for training energy-based models (EBM) with intractable normalisation terms. The key idea of NCE is to learn by comparing unnormalised log-likelihoods of the reference and noisy samples, thus avoiding explicitly computing normalisation terms. However, NCE critically relies on the quality of noisy samples. Recently, sliced score matching (SSM) has been popularised by closely related diffusion models (DM). Unlike NCE, SSM learns a gradient of log-likelihood, or score, by learning distribution of its projections on randomly chosen directions. However, both NCE and SSM disregard the form of log-likelihood function, which is problematic given that EBMs and DMs make use of first-order optimisation during inference. This paper proposes a new criterion that learns scores more suitable for first-order schemes. Experiments contrasts these approaches for training EBMs.

Energy-Based Models (EBMs) provide an interpretable framework for generative modeling of scientific data, but poor Markov Chain Monte Carlo mixing often limits their reliability. We introduce a training algorithm based on Parallel Trajectory Tempering (PTT), which exploits the continuity of the optimization path to maintain equilibrium sampling throughout learning. This enables stable and fast training on highly multimodal and data-scarce scientific datasets. Combined with reservoir sampling and adaptive optimization, PTT has a computational cost comparable to Persistent Contrastive Divergence, making it a practical replacement for standard training methods. It also provides direct estimates of thermalization times, equilibrium samples from trained models, and accurate log-likelihoods at essentially no additional cost. Experiments on Restricted Boltzmann Machines show that PTT consistently outperforms existing EBM training approaches. On discrete tabular data, it also surpasses state-of-the-art deep generative models, yielding higher-quality samples and greater robustness to overfitting and limited data. Our results make equilibrium maximum-likelihood training of EBMs practical and computationally efficient.

Autoregressive (AR) models with diffusion heads have recently achieved strong text-to-audio performance, yet their iterative decoding and multi-step sampling process introduce high-latency issues. To address this bottleneck, we propose a one-step sampling framework that combines an energy-distance training objective with representation-level distillation. An energy-scoring head maps Gaussian noise directly to audio latents in one step, eliminating the need for a costly recursive diffusion sampling process, while distillation from a masked autoregressive (MAR) text-to-audio model preserves the strong conditioning learned during diffusion training. On the AudioCaps benchmark, our method consistently outperforms prior one-step baselines such as ConsistencyTTA, SoundCTM, AudioLCM and AudioTurbo, on both objective and subjective metrics, while substantially narrowing the quality gap to AR diffusion systems with multi-step sampling. Compared to the state-of-the-art AR diffusion system, IMPACT, our approach achieves up to $8.5$x faster batch inference with highly competitive audio quality. These results demonstrate that combining energy-distance training with representation-level distillation provides an effective recipe for fast, high-quality text-to-audio synthesis.