Singing voice synthesis (SVS) aims to produce high-fidelity singing audio from music scores, requiring a detailed understanding of notes, pitch, and duration, unlike text-to-speech tasks. Although diffusion models have shown exceptional performance in various generative tasks like image and video creation, their application in SVS is hindered by time complexity and the challenge of capturing acoustic features, particularly during pitch transitions. Some networks learn from the prior distribution and use the compressed latent state as a better start in the diffusion model, but the denoising step doesn't consistently improve quality over the entire duration. We introduce RDSinger, a reference-based denoising diffusion network that generates high-quality audio for SVS tasks. Our approach is inspired by Animate Anyone, a diffusion image network that maintains intricate appearance features from reference images. RDSinger utilizes FastSpeech2 mel-spectrogram as a reference to mitigate denoising step artifacts. Additionally, existing models could be influenced by misleading information on the compressed latent state during pitch transitions. We address this issue by applying Gaussian blur on partial reference mel-spectrogram and adjusting loss weights in these regions. Extensive ablation studies demonstrate the efficiency of our method. Evaluations on OpenCpop, a Chinese singing dataset, show that RDSinger outperforms current state-of-the-art SVS methods in performance.

The long runtime of high-fidelity partial differential equation (PDE) solvers makes them unsuitable for time-critical applications. We propose to accelerate PDE solvers using reduced-order modeling (ROM). Whereas prior ROM approaches reduce the dimensionality of discretized vector fields, our continuous reduced-order modeling (CROM) approach builds a low-dimensional embedding of the continuous vector fields themselves, not their discretization. We represent this reduced manifold using continuously differentiable neural fields, which may train on any and all available numerical solutions of the continuous system, even when they are obtained using diverse methods or discretizations. We validate our approach on an extensive range of PDEs with training data from voxel grids, meshes, and point clouds. Compared to prior discretization-dependent ROM methods, such as linear subspace proper orthogonal decomposition (POD) and nonlinear manifold neural-network-based autoencoders, CROM features higher accuracy, lower memory consumption, dynamically adaptive resolutions, and applicability to any discretization. For equal latent space dimension, CROM exhibits 79$\times$ and 49$\times$ better accuracy, and 39$\times$ and 132$\times$ smaller memory footprint, than POD and autoencoder methods, respectively. Experiments demonstrate 109$\times$ and 89$\times$ wall-clock speedups over unreduced models on CPUs and GPUs, respectively. Videos and codes are available on the project page: https://crom-pde.github.io