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Diffusion-based generative models (DBGMs) perturb data to a target noise distribution and reverse this process to generate samples. The choice of noising process, or inference diffusion process, affects both likelihoods and sample quality.…
This paper considers a GI/GI/1 processor sharing queue in which jobs have soft deadlines. At each point in time, the collection of residual service times and deadlines is modeled using a random counting measure on the right half-plane. The…
Today, network devices share buffer across priority queues to avoid drops during transient congestion. While cost-effective most of the time, this sharing can cause undesired interference among seemingly independent traffic. As a result,…
Scheduling and managing queues with bounded buffers are among the most fundamental problems in computer networking. Traditionally, it is often assumed that all the properties of each packet are known immediately upon arrival. However, as…
We consider the problem of designing a packet-level congestion control and scheduling policy for datacenter networks. Current datacenter networks primarily inherit the principles that went into the design of Internet, where congestion…
This paper studies many-server limits for multi-server queues that have a phase-type service time distribution and allow for customer abandonment. The first set of limit theorems is for critically loaded $G/Ph/n+GI$ queues, where the…
This paper investigates the problem of distributed stochastic approximation in multi-agent systems. The algorithm under study consists of two steps: a local stochastic approximation step and a diffusion step which drives the network to a…
Mean-field limits have been used now as a standard tool in approximations, including for networks with a large number of nodes. Statistical inference on mean-filed models has attracted more attention recently mainly due to the rapid…
Motivated by queues with many servers, we study Brownian steady-state approximations for continuous time Markov chains (CTMCs). Our approximations are based on diffusion models (rather than a diffusion limit) whose steady-state, we prove,…
Text-to-image generation using diffusion models has seen explosive popularity owing to their ability in producing high quality images adhering to text prompts. However, production-grade diffusion model serving is a resource intensive task…
Randomized load balancing networks arise in a variety of applications, and allow for efficient sharing of resources, while being relatively easy to implement. We consider a network of parallel queues in which incoming jobs with independent…
We present Linear Diffusion Networks (LDNs), a novel architecture that reinterprets sequential data processing as a unified diffusion process. Our model integrates adaptive diffusion modules with localized nonlinear updates and a…
This paper proposes and analyzes a novel clustering algorithm that combines graph-based diffusion geometry with techniques based on density and mode estimation. The proposed method is suitable for data generated from mixtures of…
Diffusion models have recently revolutionized the field of image synthesis due to their ability to generate photorealistic images. However, one of the major drawbacks of diffusion models is that the image generation process is costly. A…
This paper investigates a partially observable queueing system with $N$ nodes in which each node has a dedicated arrival stream. There is an extra arrival stream to balance the load of the system by routing its customers to the shortest…
Tandem queueing networks are widely used to model systems where services are provided in sequential stages. In this study, we assume that each station in the tandem system operates under a general renewal process. Additionally, we assume…
We consider a one-dimensional stochastic reaction-diffusion generalizing the totally asymmetric simple exclusion process, and aiming at describing single lane roads with vehicles that can change speed. To each particle is associated a jump…
Systems of reaction-diffusion equations are commonly used in biological models of food chains. The populations and their complicated interactions present numerous challenges in theory and in numerical approximation. In particular,…
Scene flow estimation is an essential ingredient for a variety of real-world applications, especially for autonomous agents, such as self-driving cars and robots. While recent scene flow estimation approaches achieve a reasonable accuracy,…
Clustering algorithms partition a dataset into groups of similar points. The clustering problem is very general, and different partitions of the same dataset could be considered correct and useful. To fully understand such data, it must be…