Diffusion probabilistic models (DPMs) are a new class of generative models that have achieved state-of-the-art generation quality in various domains. Despite the promise, one major drawback of DPMs is the slow generation speed due to the large number of neural network evaluations required in the generation process. In this paper, we reveal an overlooked dimension -- model schedule -- for optimizing the trade-off between generation quality and speed. More specifically, we observe that small models, though having worse generation quality when used alone, could outperform large models in certain generation steps. Therefore, unlike the traditional way of using a single model, using different models in different generation steps in a carefully designed \emph{model schedule} could potentially improve generation quality and speed \emph{simultaneously}. We design OMS-DPM, a predictor-based search algorithm, to optimize the model schedule given an arbitrary generation time budget and a set of pre-trained models. We demonstrate that OMS-DPM can find model schedules that improve generation quality and speed than prior state-of-the-art methods across CIFAR-10, CelebA, ImageNet, and LSUN datasets. When applied to the public checkpoints of the Stable Diffusion model, we are able to accelerate the sampling by 2$\times$ while maintaining the generation quality.

Many applications require the collection of data on different variables or measurements overa number of system performance metrics. For example, some cyber systems rely on scanning various system metrics to detect or to predict potential cyber intrusions or threats. In the maintenance of airplanes or major factorymachinery, measurements of different system components and their usage statistics are collected to determine when a maintenance is required. In medical diagnosis, a patient may be asked to take various medical tests, such 1 as on blood pressure, cholesterol level, heart rates and so on, so that the doctor coulddetermine if the patient has a certain disease. In the development of an e-commerce product that predicts the click or purchase of a product at an e-commerce website, many data related to a user's shopping behavior will be collected, and often extra data relevant to the product or the user's shopping behavior are purchased from a third-party vendor etc. The data collected on various measures need to be combined, and if cost is a concern, a subset of measures need to be selected to satisfy the budget constraint. The problem of combining measures for a target application can be formulated as follows.