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Michael Elad

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19 papers

2 author rows

ICML Conference 2025 Conference Paper

Compressed Image Generation with Denoising Diffusion Codebook Models

Guy Ohayon
Hila Manor
Tomer Michaeli
Michael Elad

We present a novel generative approach based on Denoising Diffusion Models (DDMs), which produces high-quality image samples along with their losslessly compressed bit-stream representations. This is obtained by replacing the standard Gaussian noise sampling in the reverse diffusion with a selection of noise samples from pre-defined codebooks of fixed iid Gaussian vectors. Surprisingly, we find that our method, termed Denoising Diffusion Codebook Model (DDCM), retains sample quality and diversity of standard DDMs, even for extremely small codebooks. We leverage DDCM and pick the noises from the codebooks that best match a given image, converting our generative model into a highly effective lossy image codec achieving state-of-the-art perceptual image compression results. More generally, by setting other noise selections rules, we extend our compression method to any conditional image generation task (e. g. , image restoration), where the generated images are produced jointly with their condensed bit-stream representations. Our work is accompanied by a mathematical interpretation of the proposed compressed conditional generation schemes, establishing a connection with score-based approximations of posterior samplers for the tasks considered. Code and demo are available on our project’s website.

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ICLR Conference 2025 Conference Paper

Posterior-Mean Rectified Flow: Towards Minimum MSE Photo-Realistic Image Restoration

Guy Ohayon
Tomer Michaeli
Michael Elad

Photo-realistic image restoration algorithms are typically evaluated by distortion measures (e.g., PSNR, SSIM) and by perceptual quality measures (e.g., FID, NIQE), where the desire is to attain the lowest possible distortion without compromising on perceptual quality. To achieve this goal, current methods commonly attempt to sample from the posterior distribution, or to optimize a weighted sum of a distortion loss (e.g., MSE) and a perceptual quality loss (e.g., GAN). Unlike previous works, this paper is concerned specifically with the *optimal* estimator that minimizes the MSE under a constraint of perfect perceptual index, namely where the distribution of the reconstructed images is equal to that of the ground-truth ones. A recent theoretical result shows that such an estimator can be constructed by optimally transporting the posterior mean prediction (MMSE estimate) to the distribution of the ground-truth images. Inspired by this result, we introduce Posterior-Mean Rectified Flow (PMRF), a simple yet highly effective algorithm that approximates this optimal estimator. In particular, PMRF first predicts the posterior mean, and then transports the result to a high-quality image using a rectified flow model that approximates the desired optimal transport map. We investigate the theoretical utility of PMRF and demonstrate that it consistently outperforms previous methods on a variety of image restoration tasks.

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TMLR Journal 2025 Journal Article

PSC: Posterior Sampling-Based Compression

Noam Elata
Tomer Michaeli
Michael Elad

Diffusion models have transformed the landscape of image generation and now show remarkable potential for image compression. Most of the recent diffusion-based compression methods require training and are tailored for a specific bit-rate. In this work, we propose Posterior Sampling-based Compression (PSC) -- a zero-shot compression method that leverages a pre-trained diffusion model as its sole neural network component, thus enabling the use of diverse, publicly available models without additional training. Our approach is inspired by transform coding methods, which encode the image in some pre-chosen transform domain. However, PSC constructs a transform that is adaptive to the image. This is done by employing a zero-shot diffusion-based posterior sampler so as to progressively construct the rows of the transform matrix. Each new chunk of rows is chosen to reduce the uncertainty about the image given the quantized measurements collected thus far. Importantly, the same adaptive scheme can be replicated at the decoder, thus avoiding the need to encode the transform itself. We demonstrate that even with basic quantization and entropy coding, PSC's performance is comparable to established training-based methods in terms of rate, distortion, and perceptual quality. This is while providing greater flexibility, allowing to choose at inference time any desired rate or distortion.

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TMLR Journal 2025 Journal Article

Text-to-Image Generation Via Energy-Based CLIP

Roy Ganz
Michael Elad

Joint Energy Models (JEMs), while drawing significant research attention, have not been successfully scaled to real-world, high-resolution datasets. We present CLIP-JEM, a novel approach extending JEMs to the multimodal vision-language domain using CLIP, integrating both generative and discriminative objectives. For the generative one, we introduce an image-text joint-energy function based on Cosine similarity in the CLIP space, training CLIP to assign low energy to real image-caption pairs and high energy otherwise. For the discriminative one, we employ contrastive adversarial loss, extending the adversarial training objective to the multimodal domain. CLIP-JEM not only generates realistic images from text but also achieves competitive results on the compositionality benchmark, outperforming leading methods with fewer parameters. Additionally, we demonstrate the superior guidance capability of CLIP-JEM by enhancing CLIP-based generative frameworks and converting unconditional diffusion models to text-based ones. Lastly, we show that our model can serve as a more robust evaluation metric for text-to-image generative tasks than CLIP.

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ICLR Conference 2024 Conference Paper

DiffAR: Denoising Diffusion Autoregressive Model for Raw Speech Waveform Generation

Roi Benita
Michael Elad
Joseph Keshet

Diffusion models have recently been shown to be relevant for high-quality speech generation. Most work has been focused on generating spectrograms, and as such, they further require a subsequent model to convert the spectrogram to a waveform (i.e., a vocoder). This work proposes a diffusion probabilistic end-to-end model for generating a raw speech waveform. The proposed model is autoregressive, generating overlapping frames sequentially, where each frame is conditioned on a portion of the previously generated one. Hence, our model can effectively synthesize an unlimited speech duration while preserving high-fidelity synthesis and temporal coherence. We implemented the proposed model for unconditional and conditional speech generation, where the latter can be driven by an input sequence of phonemes, amplitudes, and pitch values. Working on the waveform directly has some empirical advantages. Specifically, it allows the creation of local acoustic behaviors, like vocal fry, which makes the overall waveform sounds more natural. Furthermore, the proposed diffusion model is stochastic and not deterministic; therefore, each inference generates a slightly different waveform variation, enabling abundance of valid realizations. Experiments show that the proposed model generates speech with superior quality compared with other state-of-the-art neural speech generation systems.

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ICML Conference 2024 Conference Paper

Early Time Classification with Accumulated Accuracy Gap Control

Liran Ringel
Regev Cohen
Daniel Freedman
Michael Elad
Yaniv Romano

Early time classification algorithms aim to label a stream of features without processing the full input stream, while maintaining accuracy comparable to that achieved by applying the classifier to the entire input. In this paper, we introduce a statistical framework that can be applied to any sequential classifier, formulating a calibrated stopping rule. This data-driven rule attains finite-sample, distribution-free control of the accuracy gap between full and early-time classification. We start by presenting a novel method that builds on the Learn-then-Test calibration framework to control this gap marginally, on average over i. i. d. instances. As this algorithm tends to yield an excessively high accuracy gap for early halt times, our main contribution is the proposal of a framework that controls a stronger notion of error, where the accuracy gap is controlled conditionally on the accumulated halt times. Numerical experiments demonstrate the effectiveness, applicability, and usefulness of our method. We show that our proposed early stopping mechanism reduces up to 94% of timesteps used for classification while achieving rigorous accuracy gap control.

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NeurIPS Conference 2024 Conference Paper

Enhancing Consistency-Based Image Generation via Adversarialy-Trained Classification and Energy-Based Discrimination

Shelly Golan
Roy Ganz
Michael Elad

The recently introduced Consistency models pose an efficient alternative to diffusion algorithms, enabling rapid and good quality image synthesis. These methods overcome the slowness of diffusion models by directly mapping noise to data, while maintaining a (relatively) simpler training. Consistency models enable a fast one- or few-step generation, but they typically fall somewhat short in sample quality when compared to their diffusion origins. In this work we propose a novel and highly effective technique for post-processing Consistency-based generated images, enhancing their perceptual quality. Our approach utilizes a joint classifier-discriminator model, in which both portions are trained adversarially. While the classifier aims to grade an image based on its assignment to a designated class, the discriminator portion of the very same network leverages the softmax values to assess the proximity of the input image to the targeted data manifold, thereby serving as an Energy-based Model. By employing example-specific projected gradient iterations under the guidance of this joint machine, we refine synthesized images and achieve an improved FID scores on the ImageNet 64x64 dataset for both Consistency-Training and Consistency-Distillation techniques.

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TMLR Journal 2024 Journal Article

GSURE-Based Diffusion Model Training with Corrupted Data

Bahjat Kawar
Noam Elata
Tomer Michaeli
Michael Elad

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.

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NeurIPS Conference 2024 Conference Paper

Perceptual Fairness in Image Restoration

Guy Ohayon
Michael Elad
Tomer Michaeli

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.

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ICML Conference 2024 Conference Paper

The Perception-Robustness Tradeoff in Deterministic Image Restoration

Guy Ohayon
Tomer Michaeli
Michael Elad

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.

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TMLR Journal 2023 Journal Article

BIGRoC: Boosting Image Generation via a Robust Classifier

Roy Ganz
Michael Elad

The interest of the machine learning community in image synthesis has grown significantly in recent years, with the introduction of a wide range of deep generative models and means for training them. In this work, we propose a general model-agnostic technique for improving the image quality and the distribution fidelity of generated images obtained by any generative model. Our method, termed BIGRoC (Boosting Image Generation via a Robust Classifier), is based on a post-processing procedure via the guidance of a given robust classifier and without a need for additional training of the generative model. Given a synthesized image, we propose to update it through projected gradient steps over the robust classifier to refine its recognition. We demonstrate this post-processing algorithm on various image synthesis methods and show a significant quantitative and qualitative improvement on CIFAR-10 and ImageNet. Surprisingly, although BIGRoC is the first model agnostic among refinement approaches and requires much less information, it outperforms competitive methods. Specifically, BIGRoC improves the image synthesis best performing diffusion model on ImageNet $128\times128$ by 14.81%, attaining an FID score of 2.53 and on $256\times256$ by 7.87%, achieving an FID of 3.63. Moreover, we conduct an opinion survey, according to which humans significantly prefer our method's outputs.

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NeurIPS Conference 2023 Conference Paper

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

Theo Adrai
Guy Ohayon
Michael Elad
Tomer Michaeli

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 that of 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 with arbitrary dimensions.

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ICML Conference 2023 Conference Paper

Do Perceptually Aligned Gradients Imply Robustness?

Roy Ganz
Bahjat Kawar
Michael Elad

Adversarially robust classifiers possess a trait that non-robust models do not - Perceptually Aligned Gradients (PAG). Their gradients with respect to the input align well with human perception. Several works have identified PAG as a byproduct of robust training, but none have considered it as a standalone phenomenon nor studied its own implications. In this work, we focus on this trait and test whether Perceptually Aligned Gradients imply Robustness. To this end, we develop a novel objective to directly promote PAG in training classifiers and examine whether models with such gradients are more robust to adversarial attacks. Extensive experiments on multiple datasets and architectures validate that models with aligned gradients exhibit significant robustness, exposing the surprising bidirectional connection between PAG and robustness. Lastly, we show that better gradient alignment leads to increased robustness and harness this observation to boost the robustness of existing adversarial training techniques.

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TMLR Journal 2023 Journal Article

Enhancing Diffusion-Based Image Synthesis with Robust Classifier Guidance

Bahjat Kawar
Roy Ganz
Michael Elad

Denoising diffusion probabilistic models (DDPMs) are a recent family of generative models that achieve state-of-the-art results. In order to obtain class-conditional generation, it was suggested to guide the diffusion process by gradients from a time-dependent classifier. While the idea is theoretically sound, deep learning-based classifiers are infamously susceptible to gradient-based adversarial attacks. Therefore, while traditional classifiers may achieve good accuracy scores, their gradients are possibly unreliable and might hinder the improvement of the generation results. Recent work discovered that adversarially robust classifiers exhibit gradients that are aligned with human perception, and these could better guide a generative process towards semantically meaningful images. We utilize this observation by defining and training a time-dependent adversarially robust classifier and use it as guidance for a generative diffusion model. In experiments on the highly challenging and diverse ImageNet dataset, our scheme introduces significantly more intelligible intermediate gradients, better alignment with theoretical findings, as well as improved generation results under several evaluation metrics. Furthermore, we conduct an opinion survey whose findings indicate that human raters prefer our method's results.

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ICML Conference 2023 Conference Paper

Reasons for the Superiority of Stochastic Estimators over Deterministic Ones: Robustness, Consistency and Perceptual Quality

Guy Ohayon
Theo Joseph Adrai
Michael Elad
Tomer Michaeli

Stochastic restoration algorithms allow to explore the space of solutions that correspond to the degraded input. In this paper we reveal additional fundamental advantages of stochastic methods over deterministic ones, which further motivate their use. First, we prove that any restoration algorithm that attains perfect perceptual quality and whose outputs are consistent with the input must be a posterior sampler, and is thus required to be stochastic. Second, we illustrate that while deterministic restoration algorithms may attain high perceptual quality, this can be achieved only by filling up the space of all possible source images using an extremely sensitive mapping, which makes them highly vulnerable to adversarial attacks. Indeed, we show that enforcing deterministic models to be robust to such attacks profoundly hinders their perceptual quality, while robustifying stochastic models hardly influences their perceptual quality, and improves their output variability. These findings provide a motivation to foster progress in stochastic restoration methods, paving the way to better recovery algorithms.

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NeurIPS Conference 2022 Conference Paper

Denoising Diffusion Restoration Models

Bahjat Kawar
Michael Elad
Stefano Ermon
Jiaming Song

Many interesting tasks in image restoration can be cast as linear inverse problems. A recent family of approaches for solving these problems uses stochastic algorithms that sample from the posterior distribution of natural images given the measurements. However, efficient solutions often require problem-specific supervised training to model the posterior, whereas unsupervised methods that are not problem-specific typically rely on inefficient iterative methods. This work addresses these issues by introducing Denoising Diffusion Restoration Models (DDRM), an efficient, unsupervised posterior sampling method. Motivated by variational inference, DDRM takes advantage of a pre-trained denoising diffusion generative model for solving any linear inverse problem. We demonstrate DDRM's versatility on several image datasets for super-resolution, deblurring, inpainting, and colorization under various amounts of measurement noise. DDRM outperforms the current leading unsupervised methods on the diverse ImageNet dataset in reconstruction quality, perceptual quality, and runtime, being $5\times$ faster than the nearest competitor. DDRM also generalizes well for natural images out of the distribution of the observed ImageNet training set.

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NeurIPS Conference 2021 Conference Paper

SNIPS: Solving Noisy Inverse Problems Stochastically

Bahjat Kawar
Gregory Vaksman
Michael Elad

In this work we introduce a novel stochastic algorithm dubbed SNIPS, which draws samples from the posterior distribution of any linear inverse problem, where the observation is assumed to be contaminated by additive white Gaussian noise. Our solution incorporates ideas from Langevin dynamics and Newton's method, and exploits a pre-trained minimum mean squared error (MMSE) Gaussian denoiser. The proposed approach relies on an intricate derivation of the posterior score function that includes a singular value decomposition (SVD) of the degradation operator, in order to obtain a tractable iterative algorithm for the desired sampling. Due to its stochasticity, the algorithm can produce multiple high perceptual quality samples for the same noisy observation. We demonstrate the abilities of the proposed paradigm for image deblurring, super-resolution, and compressive sensing. We show that the samples produced are sharp, detailed and consistent with the given measurements, and their diversity exposes the inherent uncertainty in the inverse problem being solved.

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NeurIPS Conference 2019 Conference Paper

Rethinking the CSC Model for Natural Images

Dror Simon
Michael Elad

Sparse representation with respect to an overcomplete dictionary is often used when regularizing inverse problems in signal and image processing. In recent years, the Convolutional Sparse Coding (CSC) model, in which the dictionary consists of shift invariant filters, has gained renewed interest. While this model has been successfully used in some image processing problems, it still falls behind traditional patch-based methods on simple tasks such as denoising. In this work we provide new insights regarding the CSC model and its capability to represent natural images, and suggest a Bayesian connection between this model and its patch-based ancestor. Armed with these observations, we suggest a novel feed-forward network that follows an MMSE approximation process to the CSC model, using strided convolutions. The performance of this supervised architecture is shown to be on par with state of the art methods while using much fewer parameters.

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JMLR Journal 2017 Journal Article

Convolutional Neural Networks Analyzed via Convolutional Sparse Coding

Vardan Papyan
Yaniv Romano
Michael Elad

Convolutional neural networks (CNN) have led to many state-of- the-art results spanning through various fields. However, a clear and profound theoretical understanding of the forward pass, the core algorithm of CNN, is still lacking. In parallel, within the wide field of sparse approximation, Convolutional Sparse Coding (CSC) has gained increasing attention in recent years. A theoretical study of this model was recently conducted, establishing it as a reliable and stable alternative to the commonly practiced patch-based processing. Herein, we propose a novel multi-layer model, ML-CSC, in which signals are assumed to emerge from a cascade of CSC layers. This is shown to be tightly connected to CNN, so much so that the forward pass of the CNN is in fact the thresholding pursuit serving the ML-CSC model. This connection brings a fresh view to CNN, as we are able to attribute to this architecture theoretical claims such as uniqueness of the representations throughout the network, and their stable estimation, all guaranteed under simple local sparsity conditions. Lastly, identifying the weaknesses in the above pursuit scheme, we propose an alternative to the forward pass, which is connected to deconvolutional and recurrent networks, and also has better theoretical guarantees. [abs] [ pdf ][ bib ] &copy JMLR 2017. ( edit, beta )

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