Diffusion models are powerful generative models but suffer from slow sampling, often taking 1000 sequential denoising steps for one sample. As a result, considerable efforts have been directed toward reducing the number of denoising steps, but these methods hurt sample quality. Instead of reducing the number of denoising steps (trading quality for speed), in this paper we explore an orthogonal approach: can we run the denoising steps in parallel (trading compute for speed)? In spite of the sequential nature of the denoising steps, we show that surprisingly it is possible to parallelize sampling via Picard iterations, by guessing the solution of future denoising steps and iteratively refining until convergence. With this insight, we present ParaDiGMS, a novel method to accelerate the sampling of pretrained diffusion models by denoising multiple steps in parallel. ParaDiGMS is the first diffusion sampling method that enables trading compute for speed and is even compatible with existing fast sampling techniques such as DDIM and DPMSolver. Using ParaDiGMS, we improve sampling speed by 2-4x across a range of robotics and image generation models, giving state-of-the-art sampling speeds of 0.2s on 100-step DiffusionPolicy and 14.6s on 1000-step StableDiffusion-v2 with no measurable degradation of task reward, FID score, or CLIP score.1

The architecture of LFADS is described in more detail in the original publication [1]. We used a dimension of 64 for the initial condition (IC) encoder, controller input (CI) encoder, initial condition, and controller. The controller output dimension was 2 and the generator dimension was 100. The latent factor dimensionality was 40 for the maze dataset and 100 for both calcium datasets. LFADS models benefit from appropriate hyperparameter (HP) tuning, as optimal HP combinations can vary from dataset to dataset [2, 3]. As mentioned in the main text, we use AutoLFADS [3] to ensure appropriate HP tuning. The framework combines a regularization strategy (coordinated dropout; CD [2]) with a largescale framework for optimizing model hyperparameters (population-based training; PBT [4]).

Unlike MI, some GEMINIs do not require regularisations when training.

Improving the generalization of deep networks is an important open challenge, particularly in domains without plentiful data. The mixup algorithm improves generalization by linearly interpolating a pair of examples and their corresponding labels. These interpolated examples augment the original training set. Mixup has shown promising results in various classification tasks, but systematic analysis of mixup in regression remains underexplored. Using mixup directly on regression labels can result in arbitrarily incorrect labels.