The Momentum Schr{ö}dinger Bridge (mSB) (Chen et al., 2023c) has emerged as a leading method for accelerating generative diffusion processes and reducing transport costs. However, the lack of simulation-free properties inevitably results in high training costs and affects scalability. To obtain a trade-off between transport properties and scalability, we introduce variational Schrödinger momentum diffusion (VSMD), which employs linearized forward score functions (variational scores) to eliminate the dependence on simulated forward trajectories. Our approach leverages a multivariate diffusion process with adaptively transport-optimized variational scores. Additionally, we apply a critical-damping transform to stabilize training by removing the need for score estimations for both velocity and samples. Theoretically, we prove the convergence of samples generated with optimal variational scores and momentum diffusion. Empirical results demonstrate that VSMD efficiently generates anisotropic shapes while maintaining transport efficacy, outperforming overdamped alternatives, and avoiding complex denoising processes. Our approach also scales effectively to real-world data, achieving competitive results in time series and image generation, both in unconditional and conditional settings.

Diffusion models have demonstrated remarkable performance in generating unimodal data across various tasks, including image, video, and text generation. On the contrary, the joint generation of multimodal data through diffusion models is still in the early stages of exploration. Existing approaches heavily rely on external preprocessing protocols, such as tokenizers and variational autoencoders, to harmonize varied data representations into a unified, unimodal format. This process heavily demands the high accuracy of encoders and decoders, which can be problematic for applications with limited data. To lift this restriction, we propose a novel framework for building multimodal diffusion models on arbitrary state spaces, enabling native generation of coupled data across different modalities. By introducing an innovative decoupled noise schedule for each modality, we enable both unconditional and modality-conditioned generation within a single model simultaneously. We empirically validate our approach for text-image generation and mixed-type tabular data synthesis, demonstrating that it achieves competitive performance. Code is available at https://github.com/KevinRojas1499/Diffuse-Everything.

This paper considers the problem of sampling from non-logconcave distribution, based on queries of its unnormalized density. It first describes a framework, Denoising Diffusion Monte Carlo (DDMC), based on the simulation of a denoising diffusion process with its score function approximated by a generic Monte Carlo estimator. DDMC is an oracle-based meta-algorithm, where its oracle is the assumed access to samples that generate a Monte Carlo score estimator. Then we provide an implementation of this oracle, based on rejection sampling, and this turns DDMC into a true algorithm, termed Zeroth-Order Diffusion Monte Carlo (ZOD-MC). We provide convergence analyses by first constructing a general framework, i.e. a performance guarantee for DDMC, without assuming the target distribution to be log-concave or satisfying any isoperimetric inequality. Then we prove that ZOD-MC admits an inverse polynomial dependence on the desired sampling accuracy, albeit still suffering from the curse of dimensionality. Consequently, for low dimensional distributions, ZOD-MC is a very efficient sampler, with performance exceeding latest samplers, including also-denoising-diffusion-based RDMC and RSDMC. Last, we experimentally demonstrate the insensitivity of ZOD-MC to increasingly higher barriers between modes or discontinuity in non-convex potential.