Score-based diffusion models are a class of generative models whose dynamics is described by stochastic differential equations that map noise into data. While recent works have started to lay down a theoretical foundation for these models, a detailed understanding of the role of the diffusion time T is still lacking. Current best practice advocates for a large T to ensure that the forward dynamics brings the diffusion sufficiently close to a known and simple noise distribution; however, a smaller value of T should be preferred for a better approximation of the score-matching objective and higher computational efficiency. Starting from a variational interpretation of diffusion models, in this work we quantify this trade-off and suggest a new method to improve quality and efficiency of both training and sampling, by adopting smaller diffusion times. Indeed, we show how an auxiliary model can be used to bridge the gap between the ideal and the simulated forward dynamics, followed by a standard reverse diffusion process. Empirical results support our analysis; for image data, our method is competitive with regard to the state of the art, according to standard sample quality metrics and log-likelihood.

Cache policies to minimize the content retrieval cost have been studied through competitive analysis when the miss costs are additive and the sequence of content requests is arbitrary. More recently, a cache utility maximization problem has been introduced, where contents have stationary popularities and utilities are strictly concave in the hit rates. This paper bridges the two formulations, considering linear costs and content popularities. We show that minimizing the retrieval cost corresponds to solving an online knapsack problem, and we propose new dynamic policies inspired by simulated annealing, including DYNQLRU, a variant of QLRU. We prove that DynqLRU asymptotically asymptotic converges to the optimum under the characteristic time approximation. In a real scenario, popularities vary over time and their estimation is very difficult. DYNQLRU does not require popularity estimation, and our realistic, trace-driven evaluation shows that it significantly outperforms state-of-the-art policies, with up to 45% cost reduction.

We consider elastic resource provisioning in the cloud, focusing on in-memory key-value stores used as caches. Our goal is to dynamically scale resources to the traffic pattern minimizing the overall cost, which includes not only the storage cost, but also the cost due to misses. In fact, a small variation of the cache miss ratio may have a significant impact on user perceived performance in modern web services, which in turn has an impact on the overall revenues for the content provider using such services. We propose and study a dynamic algorithm for TTL caches, which is able to obtain close-to-minimal costs. Since high-throughput caches require low complexity operations, we discuss a practical implementation of such a scheme requiring constant overhead per request independently from the cache size. We evaluate our solution with real-world traces collected from Akamai, and show that the TTL approach is able to track the optimal cache configuration and achieve significant cost savings specially in highly dynamic settings that are likely to require elastic cloud services.

Multimodal datasets are ubiquitous in modern applications, and multimodal Variational Autoencoders are a popular family of models that aim to learn a joint representation of different modalities. However, existing approaches suffer from a coherence–quality tradeoff in which models with good generation quality lack generative coherence across modalities and vice versa. In this paper, we discuss the limitations underlying the unsatisfactory performance of existing methods in order to motivate the need for a different approach. We propose a novel method that uses a set of independently trained and unimodal deterministic autoencoders. Individual latent variables are concatenated into a common latent space, which is then fed to a masked diffusion model to enable generative modeling. We introduce a new multi-time training method to learn the conditional score network for multimodal diffusion. Our methodology substantially outperforms competitors in both generation quality and coherence, as shown through an extensive experimental campaign.