Music Restoration via Latent Operator Optimization and Diffusion Model Priors

Music restoration seeks to recover a clean signal from an observed recording degraded by an unknown effect, distortion, or corruption. Existing systems often rely on paired training data and distortion-specific supervision, which limits their use when the forward process is not known in advance. We propose LOUDAR (Latent-space Optimization of Unknown Distortion for Audio Restoration) a general-purpose restoration method that operates in the latent space of a pretrained audio autoencoder and models the unknown distortion as a learnable latent operator. At inference time, LOUDAR alternates between estimating the clean latent variable and updating the latent operator parameters. An unconditional latent diffusion model provides a prior over clean audio and regularizes this inference by steering the latent estimate toward the manifold of clean recordings. Because the degradation model is adapted per input, the approach is broadly applicable across diverse restoration problems. We evaluate LOUDAR on singing voice effect removal and restoration, as well as guitar distortion removal, and show that it consistently improves over degraded inputs and is competitive with supervised and unsupervised baselines in waveform and latent domains.

Decoupled Latent Optimization of Diffusion Models for Full Waveform Inversion

Full waveform inversion (FWI) recovers subsurface velocity from seismic recordings by solving a severely ill-posed, nonconvex PDE-constrained optimization. Classical regularizers stabilize the inversion but fail to reproduce realistic geological structures; recent diffusion-prior methods improve realism at the cost of a fragile trade-off between data fidelity and prior consistency. We propose Decoupled Latent Optimization (DLO), which relaxes the standard latent-optimization formulation into a quadratic-penalty objective over an auxiliary physical variable and a latent variable. The data-fidelity gradient acts in physical space, the diffusion sampler contributes only through a decoded prior sample, and the standard smoothed-velocity initialization of classical FWI is preserved. On the OpenFWI benchmark, DLO outperforms classical regularizers and existing diffusion-based methods under clean, noisy, and missing-trace acquisitions. The prior, trained on 70*70 OpenFWI models, transfers directly to the Marmousi and Overthrust benchmarks, where DLO recovers intricate fault structures and remains robust to initialization smoothing and measurement noise.

Geometry-Aware Neural Optimizer for Shape Optimization and Inversion

Geometry is central to PDE-governed systems, motivating shape optimization and inversion. Classical pipelines conduct costly forward simulation with geometry processing, requiring substantial expert effort. Neural surrogates accelerate forward analysis but do not close the loop because gradients from objectives to geometry are often unavailable. Existing differentiable methods either rely on restrictive parameterizations or unstable latent optimization driven by scalar objectives, limiting interpretability and part-wise control. To address these challenges, we propose Geometry-Aware Neural Optimizer (GANO), an end-to-end differentiable framework that unifies geometry representation, field-level prediction, and automated optimization/inversion in a single latent-space loop. GANO encodes shapes with an auto-decoder and stabilizes latent updates via a denoising mechanism, and a geometry-injected surrogate provides a reliable gradient pathway for geometry updates. Moreover, GANO supports part-wise control through null-space projection and uses remeshing-free projection to accelerate geometry processing. We further prove that denoising induces an implicit Jacobian regularization that reduces decoder sensitivity, yielding controlled deformations. Experiments on three benchmarks spanning 2D Helmholtz, 2D airfoil, and 3D vehicles show state-of-the-art accuracy and stable, controllable updates, achieving up to +55.9% lift-to-drag improvement for airfoils and ~7% drag reduction for vehicles.

ResetEdit: Precise Text-guided Editing of Generated Image via Resettable Starting Latent

Recent advances in diffusion models have enabled high-quality image generation, leading to increasing demand for post-generation editing that modifies local regions while preserving global structure. Achieving such flexible and precise editing requires a high-quality starting point, a latent representation that provides both the freedom needed for diverse modifications and the precision required for fine-grained, region-specific control. However, existing inversion-based approaches such as DDIM inversion often yield unsatisfactory starting latents, resulting in degraded edit fidelity and structural inconsistency. Ideally, the most suitable editing anchor should be the original latent used during the generation process, as it inherently captures the scene's structure and semantics. Yet, storing this latent for every generated image is impractical due to massive storage and retrieval costs. To address this challenge, we propose ResetEdit, a proactive diffusion editing framework that embeds recoverable latent information directly into the generation process. By injecting the discrepancy between the clean and diffused latents into the diffusion trajectory and extracting it during inversion, ResetEdit reconstructs a resettable latent that closely approximates the true starting state. Additionally, a lightweight latent optimization module compensates for reconstruction bias caused by VAE asymmetry. Built upon Stable Diffusion, ResetEdit integrates seamlessly with existing tuning-free editing methods and consistently outperforms state-of-the-art baselines in both controllability and visual fidelity.