arXiv subjects

Tomer Michaeli

Publications and source records attributed to Tomer Michaeli.

At least 37 records · Page 2Linked to original sources

arXiv2024

Perceptual Fairness in Image Restoration

Fairness in image restoration tasks is the desire to treat different sub-groups of images equally well. Existing definitions of fairness in image restoration are highly restrictive. They consider a reconstruction to be a correct outcome for a group (e.g., women) only if it falls within the group's set of ground truth images (e.g., natural images of women); otherwise, it is considered entirely incorrect. Consequently, such definitions are prone to controversy, as errors in image restoration can manifest in various ways. In this work we offer an alternative approach towards fairness in image restoration, by considering the Group Perceptual Index (GPI), which we define as the statistical distance between the distribution of the group's ground truth images and the distribution of their reconstructions. We assess the fairness of an algorithm by comparing the GPI of different groups, and say that it achieves perfect Perceptual Fairness (PF) if the GPIs of all groups are identical. We motivate and theoretically study our new notion of fairness, draw its connection to previous ones, and demonstrate its utility on state-of-the-art face image restoration algorithms.

eess.IV↗

arXiv2024

Deep Optimal Transport: A Practical Algorithm for Photo-realistic Image Restoration

We propose an image restoration algorithm that can control the perceptual quality and/or the mean square error (MSE) of any pre-trained model, trading one over the other at test time. Our algorithm is few-shot: Given about a dozen images restored by the model, it can significantly improve the perceptual quality and/or the MSE of the model for newly restored images without further training. Our approach is motivated by a recent theoretical result that links between the minimum MSE (MMSE) predictor and the predictor that minimizes the MSE under a perfect perceptual quality constraint. Specifically, it has been shown that the latter can be obtained by optimally transporting the output of the former, such that its distribution matches the source data. Thus, to improve the perceptual quality of a predictor that was originally trained to minimize MSE, we approximate the optimal transport by a linear transformation in the latent space of a variational auto-encoder, which we compute in closed-form using empirical means and covariances. Going beyond the theory, we find that applying the same procedure on models that were initially trained to achieve high perceptual quality, typically improves their perceptual quality even further. And by interpolating the results with the original output of the model, we can improve their MSE on the expense of perceptual quality. We illustrate our method on a variety of degradations applied to general content images of arbitrary dimensions.

cs.AI↗

arXiv2024

Adaptive Compressed Sensing with Diffusion-Based Posterior Sampling

Compressed Sensing (CS) facilitates rapid image acquisition by selecting a small subset of measurements sufficient for high-fidelity reconstruction. Adaptive CS seeks to further enhance this process by dynamically choosing future measurements based on information gleaned from data that is already acquired. However, many existing frameworks are often tailored to specific tasks and require intricate training procedures. We propose AdaSense, a novel Adaptive CS approach that leverages zero-shot posterior sampling with pre-trained diffusion models. By sequentially sampling from the posterior distribution, we can quantify the uncertainty of each possible future linear measurement throughout the acquisition process. AdaSense eliminates the need for additional training and boasts seamless adaptation to diverse domains with minimal tuning requirements. Our experiments demonstrate the effectiveness of AdaSense in reconstructing facial images from a small number of measurements. Furthermore, we apply AdaSense for active acquisition of medical images in the domains of magnetic resonance imaging (MRI) and computed tomography (CT), highlighting its potential for tangible real-world acceleration.

eess.IV↗

arXiv2024

Still-Moving: Customized Video Generation without Customized Video Data

Customizing text-to-image (T2I) models has seen tremendous progress recently, particularly in areas such as personalization, stylization, and conditional generation. However, expanding this progress to video generation is still in its infancy, primarily due to the lack of customized video data. In this work, we introduce Still-Moving, a novel generic framework for customizing a text-to-video (T2V) model, without requiring any customized video data. The framework applies to the prominent T2V design where the video model is built over a text-to-image (T2I) model (e.g., via inflation). We assume access to a customized version of the T2I model, trained only on still image data (e.g., using DreamBooth or StyleDrop). Naively plugging in the weights of the customized T2I model into the T2V model often leads to significant artifacts or insufficient adherence to the customization data. To overcome this issue, we train lightweight $\textit{Spatial Adapters}$ that adjust the features produced by the injected T2I layers. Importantly, our adapters are trained on $\textit{"frozen videos"}$ (i.e., repeated images), constructed from image samples generated by the customized T2I model. This training is facilitated by a novel $\textit{Motion Adapter}$ module, which allows us to train on such static videos while preserving the motion prior of the video model. At test time, we remove the Motion Adapter modules and leave in only the trained Spatial Adapters. This restores the motion prior of the T2V model while adhering to the spatial prior of the customized T2I model. We demonstrate the effectiveness of our approach on diverse tasks including personalized, stylized, and conditional generation. In all evaluated scenarios, our method seamlessly integrates the spatial prior of the customized T2I model with a motion prior supplied by the T2V model.

cs.CV↗

arXiv2024

Exact Mean Square Linear Stability Analysis for SGD

The dynamical stability of optimization methods at the vicinity of minima of the loss has recently attracted significant attention. For gradient descent (GD), stable convergence is possible only to minima that are sufficiently flat w.r.t. the step size, and those have been linked with favorable properties of the trained model. However, while the stability threshold of GD is well-known, to date, no explicit expression has been derived for the exact threshold of stochastic GD (SGD). In this paper, we derive such a closed-form expression. Specifically, we provide an explicit condition on the step size that is both necessary and sufficient for the linear stability of SGD in the mean square sense. Our analysis sheds light on the precise role of the batch size $B$. In particular, we show that the stability threshold is monotonically non-decreasing in the batch size, which means that reducing the batch size can only decrease stability. Furthermore, we show that SGD's stability threshold is equivalent to that of a mixture process which takes in each iteration a full batch gradient step w.p. $1-p$, and a single sample gradient step w.p. $p$, where $p \approx 1/B $. This indicates that even with moderate batch sizes, SGD's stability threshold is very close to that of GD's. We also prove simple necessary conditions for linear stability, which depend on the batch size, and are easier to compute than the precise threshold. Finally, we derive the asymptotic covariance of the dynamics around the minimum, and discuss its dependence on the learning rate. We validate our theoretical findings through experiments on the MNIST dataset.

cs.LG↗

arXiv2024

GSURE-Based Diffusion Model Training with Corrupted Data

Diffusion models have demonstrated impressive results in both data generation and downstream tasks such as inverse problems, text-based editing, classification, and more. However, training such models usually requires large amounts of clean signals which are often difficult or impossible to obtain. In this work, we propose a novel training technique for generative diffusion models based only on corrupted data. We introduce a loss function based on the Generalized Stein's Unbiased Risk Estimator (GSURE), and prove that under some conditions, it is equivalent to the training objective used in fully supervised diffusion models. We demonstrate our technique on face images as well as Magnetic Resonance Imaging (MRI), where the use of undersampled data significantly alleviates data collection costs. Our approach achieves generative performance comparable to its fully supervised counterpart without training on any clean signals. In addition, we deploy the resulting diffusion model in various downstream tasks beyond the degradation present in the training set, showcasing promising results.

eess.IV↗

arXiv2024

The Perception-Robustness Tradeoff in Deterministic Image Restoration

We study the behavior of deterministic methods for solving inverse problems in imaging. These methods are commonly designed to achieve two goals: (1) attaining high perceptual quality, and (2) generating reconstructions that are consistent with the measurements. We provide a rigorous proof that the better a predictor satisfies these two requirements, the larger its Lipschitz constant must be, regardless of the nature of the degradation involved. In particular, to approach perfect perceptual quality and perfect consistency, the Lipschitz constant of the model must grow to infinity. This implies that such methods are necessarily more susceptible to adversarial attacks. We demonstrate our theory on single image super-resolution algorithms, addressing both noisy and noiseless settings. We also show how this undesired behavior can be leveraged to explore the posterior distribution, thereby allowing the deterministic model to imitate stochastic methods.

eess.IV↗

arXiv2024

Discovering Interpretable Directions in the Semantic Latent Space of Diffusion Models

Denoising Diffusion Models (DDMs) have emerged as a strong competitor to Generative Adversarial Networks (GANs). However, despite their widespread use in image synthesis and editing applications, their latent space is still not as well understood. Recently, a semantic latent space for DDMs, coined `$h$-space', was shown to facilitate semantic image editing in a way reminiscent of GANs. The $h$-space is comprised of the bottleneck activations in the DDM's denoiser across all timesteps of the diffusion process. In this paper, we explore the properties of h-space and propose several novel methods for finding meaningful semantic directions within it. We start by studying unsupervised methods for revealing interpretable semantic directions in pretrained DDMs. Specifically, we show that global latent directions emerge as the principal components in the latent space. Additionally, we provide a novel method for discovering image-specific semantic directions by spectral analysis of the Jacobian of the denoiser w.r.t. the latent code. Next, we extend the analysis by finding directions in a supervised fashion in unconditional DDMs. We demonstrate how such directions can be found by relying on either a labeled data set of real images or by annotating generated samples with a domain-specific attribute classifier. We further show how to semantically disentangle the found direction by simple linear projection. Our approaches are applicable without requiring any architectural modifications, text-based guidance, CLIP-based optimization, or model fine-tuning.

cs.CV↗

arXiv2024

Zero-Shot Unsupervised and Text-Based Audio Editing Using DDPM Inversion

Editing signals using large pre-trained models, in a zero-shot manner, has recently seen rapid advancements in the image domain. However, this wave has yet to reach the audio domain. In this paper, we explore two zero-shot editing techniques for audio signals, which use DDPM inversion with pre-trained diffusion models. The first, which we coin ZEro-shot Text-based Audio (ZETA) editing, is adopted from the image domain. The second, named ZEro-shot UnSupervized (ZEUS) editing, is a novel approach for discovering semantically meaningful editing directions without supervision. When applied to music signals, this method exposes a range of musically interesting modifications, from controlling the participation of specific instruments to improvisations on the melody. Samples and code can be found in https://hilamanor.github.io/AudioEditing/ .

cs.SD↗

arXiv2024

Hierarchical Uncertainty Exploration via Feedforward Posterior Trees

When solving ill-posed inverse problems, one often desires to explore the space of potential solutions rather than be presented with a single plausible reconstruction. Valuable insights into these feasible solutions and their associated probabilities are embedded in the posterior distribution. However, when confronted with data of high dimensionality (such as images), visualizing this distribution becomes a formidable challenge, necessitating the application of effective summarization techniques before user examination. In this work, we introduce a new approach for visualizing posteriors across multiple levels of granularity using tree-valued predictions. Our method predicts a tree-valued hierarchical summarization of the posterior distribution for any input measurement, in a single forward pass of a neural network. We showcase the efficacy of our approach across diverse datasets and image restoration challenges, highlighting its prowess in uncertainty quantification and visualization. Our findings reveal that our method performs comparably to a baseline that hierarchically clusters samples from a diffusion-based posterior sampler, yet achieves this with orders of magnitude greater speed.

cs.CV↗

arXiv2024

Slicedit: Zero-Shot Video Editing With Text-to-Image Diffusion Models Using Spatio-Temporal Slices

Text-to-image (T2I) diffusion models achieve state-of-the-art results in image synthesis and editing. However, leveraging such pretrained models for video editing is considered a major challenge. Many existing works attempt to enforce temporal consistency in the edited video through explicit correspondence mechanisms, either in pixel space or between deep features. These methods, however, struggle with strong nonrigid motion. In this paper, we introduce a fundamentally different approach, which is based on the observation that spatiotemporal slices of natural videos exhibit similar characteristics to natural images. Thus, the same T2I diffusion model that is normally used only as a prior on video frames, can also serve as a strong prior for enhancing temporal consistency by applying it on spatiotemporal slices. Based on this observation, we present Slicedit, a method for text-based video editing that utilizes a pretrained T2I diffusion model to process both spatial and spatiotemporal slices. Our method generates videos that retain the structure and motion of the original video while adhering to the target text. Through extensive experiments, we demonstrate Slicedit's ability to edit a wide range of real-world videos, confirming its clear advantages compared to existing competing methods. Webpage: https://matankleiner.github.io/slicedit/

cs.CV↗

arXiv2024

Uncertainty Visualization via Low-Dimensional Posterior Projections

In ill-posed inverse problems, it is commonly desirable to obtain insight into the full spectrum of plausible solutions, rather than extracting only a single reconstruction. Information about the plausible solutions and their likelihoods is encoded in the posterior distribution. However, for high-dimensional data, this distribution is challenging to visualize. In this work, we introduce a new approach for estimating and visualizing posteriors by employing energy-based models (EBMs) over low-dimensional subspaces. Specifically, we train a conditional EBM that receives an input measurement and a set of directions that span some low-dimensional subspace of solutions, and outputs the probability density function of the posterior within that space. We demonstrate the effectiveness of our method across a diverse range of datasets and image restoration problems, showcasing its strength in uncertainty quantification and visualization. As we show, our method outperforms a baseline that projects samples from a diffusion-based posterior sampler, while being orders of magnitude faster. Furthermore, it is more accurate than a baseline that assumes a Gaussian posterior.

cs.CV↗

arXiv2024

An Edit Friendly DDPM Noise Space: Inversion and Manipulations

Denoising diffusion probabilistic models (DDPMs) employ a sequence of white Gaussian noise samples to generate an image. In analogy with GANs, those noise maps could be considered as the latent code associated with the generated image. However, this native noise space does not possess a convenient structure, and is thus challenging to work with in editing tasks. Here, we propose an alternative latent noise space for DDPM that enables a wide range of editing operations via simple means, and present an inversion method for extracting these edit-friendly noise maps for any given image (real or synthetically generated). As opposed to the native DDPM noise space, the edit-friendly noise maps do not have a standard normal distribution and are not statistically independent across timesteps. However, they allow perfect reconstruction of any desired image, and simple transformations on them translate into meaningful manipulations of the output image (e.g. shifting, color edits). Moreover, in text-conditional models, fixing those noise maps while changing the text prompt, modifies semantics while retaining structure. We illustrate how this property enables text-based editing of real images via the diverse DDPM sampling scheme (in contrast to the popular non-diverse DDIM inversion). We also show how it can be used within existing diffusion-based editing methods to improve their quality and diversity. Webpage: https://inbarhub.github.io/DDPM_inversion

cs.CV↗

arXiv2024

From Posterior Sampling to Meaningful Diversity in Image Restoration

Image restoration problems are typically ill-posed in the sense that each degraded image can be restored in infinitely many valid ways. To accommodate this, many works generate a diverse set of outputs by attempting to randomly sample from the posterior distribution of natural images given the degraded input. Here we argue that this strategy is commonly of limited practical value because of the heavy tail of the posterior distribution. Consider for example inpainting a missing region of the sky in an image. Since there is a high probability that the missing region contains no object but clouds, any set of samples from the posterior would be entirely dominated by (practically identical) completions of sky. However, arguably, presenting users with only one clear sky completion, along with several alternative solutions such as airships, birds, and balloons, would better outline the set of possibilities. In this paper, we initiate the study of meaningfully diverse image restoration. We explore several post-processing approaches that can be combined with any diverse image restoration method to yield semantically meaningful diversity. Moreover, we propose a practical approach for allowing diffusion based image restoration methods to generate meaningfully diverse outputs, while incurring only negligent computational overhead. We conduct extensive user studies to analyze the proposed techniques, and find the strategy of reducing similarity between outputs to be significantly favorable over posterior sampling. Code and examples are available at https://noa-cohen.github.io/MeaningfulDiversityInIR.

cs.CV↗

arXiv2024

The Expected Loss of Preconditioned Langevin Dynamics Reveals the Hessian Rank

Langevin dynamics (LD) is widely used for sampling from distributions and for optimization. In this work, we derive a closed-form expression for the expected loss of preconditioned LD near stationary points of the objective function. We use the fact that at the vicinity of such points, LD reduces to an Ornstein-Uhlenbeck process, which is amenable to convenient mathematical treatment. Our analysis reveals that when the preconditioning matrix satisfies a particular relation with respect to the noise covariance, LD's expected loss becomes proportional to the rank of the objective's Hessian. We illustrate the applicability of this result in the context of neural networks, where the Hessian rank has been shown to capture the complexity of the predictor function but is usually computationally hard to probe. Finally, we use our analysis to compare SGD-like and Adam-like preconditioners and identify the regimes under which each of them leads to a lower expected loss.

cs.LG↗

arXiv2024

On the Posterior Distribution in Denoising: Application to Uncertainty Quantification

Denoisers play a central role in many applications, from noise suppression in low-grade imaging sensors, to empowering score-based generative models. The latter category of methods makes use of Tweedie's formula, which links the posterior mean in Gaussian denoising (\ie the minimum MSE denoiser) with the score of the data distribution. Here, we derive a fundamental relation between the higher-order central moments of the posterior distribution, and the higher-order derivatives of the posterior mean. We harness this result for uncertainty quantification of pre-trained denoisers. Particularly, we show how to efficiently compute the principal components of the posterior distribution for any desired region of an image, as well as to approximate the full marginal distribution along those (or any other) one-dimensional directions. Our method is fast and memory-efficient, as it does not explicitly compute or store the high-order moment tensors and it requires no training or fine tuning of the denoiser. Code and examples are available on the project webpage in https://hilamanor.github.io/GaussianDenoisingPosterior/ .

cs.CV↗

arXiv2024

Lumiere: A Space-Time Diffusion Model for Video Generation

We introduce Lumiere -- a text-to-video diffusion model designed for synthesizing videos that portray realistic, diverse and coherent motion -- a pivotal challenge in video synthesis. To this end, we introduce a Space-Time U-Net architecture that generates the entire temporal duration of the video at once, through a single pass in the model. This is in contrast to existing video models which synthesize distant keyframes followed by temporal super-resolution -- an approach that inherently makes global temporal consistency difficult to achieve. By deploying both spatial and (importantly) temporal down- and up-sampling and leveraging a pre-trained text-to-image diffusion model, our model learns to directly generate a full-frame-rate, low-resolution video by processing it in multiple space-time scales. We demonstrate state-of-the-art text-to-video generation results, and show that our design easily facilitates a wide range of content creation tasks and video editing applications, including image-to-video, video inpainting, and stylized generation.

cs.CV↗

arXiv2023

Uncertainty Quantification via Neural Posterior Principal Components

Uncertainty quantification is crucial for the deployment of image restoration models in safety-critical domains, like autonomous driving and biological imaging. To date, methods for uncertainty visualization have mainly focused on per-pixel estimates. Yet, a heatmap of per-pixel variances is typically of little practical use, as it does not capture the strong correlations between pixels. A more natural measure of uncertainty corresponds to the variances along the principal components (PCs) of the posterior distribution. Theoretically, the PCs can be computed by applying PCA on samples generated from a conditional generative model for the input image. However, this requires generating a very large number of samples at test time, which is painfully slow with the current state-of-the-art (diffusion) models. In this work, we present a method for predicting the PCs of the posterior distribution for any input image, in a single forward pass of a neural network. Our method can either wrap around a pre-trained model that was trained to minimize the mean square error (MSE), or can be trained from scratch to output both a predicted image and the posterior PCs. We showcase our method on multiple inverse problems in imaging, including denoising, inpainting, super-resolution, and biological image-to-image translation. Our method reliably conveys instance-adaptive uncertainty directions, achieving uncertainty quantification comparable with posterior samplers while being orders of magnitude faster. Code and examples are available at https://eliasnehme.github.io/NPPC/

cs.CV↗