Learned denoisers play a fundamental role in various signal generation (e.g., diffusion models) and reconstruction (e.g., compressed sensing) architectures, whose success derives from their ability to leverage low-dimensional structure in data. Existing denoising methods, however, either rely on local approximations that require a linear scan of the entire dataset or treat denoising as generic function approximation problems, often sacrificing efficiency and interpretability. We consider the problem of efficiently denoising a new noisy data point sampled from an unknown $d$-dimensional manifold $M \in \mathbb{R}^D$, using only noisy samples. This work proposes a framework for test-time efficient manifold denoising, by framing the concept of "learning-to-denoise" as "learning-to-optimize". We have two technical innovations: (i) online learning methods which learn to optimize over the manifold of clean signals using only noisy data, effectively "growing" an optimizer one sample at a time. (ii) mixed-order methods which guarantee that the learned optimizers achieve global optimality, ensuring both efficiency and near-optimal denoising performance. We corroborate these claims with theoretical analyses of both the complexity and denoising performance of mixed-order traversal. Our experiments on scientific manifolds demonstrate significantly improved complexity-performance tradeoffs compared to nearest neighbor search, which underpins existing provable denoising approaches based on exhaustive search.

Peripheral Component Interconnect Express (PCIe) is the de facto interconnect standard for high-speed peripherals and CPUs. Prototyping and optimizing PCIe devices for emerging scenarios is an ongoing challenge. Since Transaction Layer Packets (TLPs) capture device-CPU interactions, it is crucial to analyze and generate realistic TLP traces for effective device design and optimization. Generative AI offers a promising approach for creating intricate, custom TLP traces necessary for PCIe hardware and software development. However, existing models often generate impractical traces due to the absence of PCIe-specific constraints, such as TLP ordering and causality. This paper presents Phantom, the first framework that treats TLP trace generation as a generative AI problem while incorporating PCIe-specific constraints. We validate Phantom's effectiveness by generating TLP traces for an actual PCIe network interface card. Experimental results show that Phantom produces practical, large-scale TLP traces, significantly outperforming existing models, with improvements of up to 1000$\times$ in task-specific metrics and up to 2.19$\times$ in Frechet Inception Distance (FID) compared to backbone-only methods.