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

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 typically 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.

Text-to-Image Generation Via Energy-Based CLIP

Joint Energy Models (JEMs), while drawing significant research attention, have not been successfully scaled to real-world, high-resolution datasets. We present EB-CLIP, a novel approach extending JEMs to the multimodal vision-language domain using CLIP, integrating both generative and discriminative objectives. For the generative objective, 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 objective, we employ contrastive adversarial loss, extending the adversarial training objective to the multimodal domain. EB-CLIP 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 EB-CLIP by enhancing CLIP-based generative frameworks and converting unconditional diffusion models to text-based ones. Lastly, we show that EB-CLIP can serve as a more robust evaluation metric for text-to-image generative tasks than CLIP.

Anchored Diffusion for Video Face Reenactment

Video generation has drawn significant interest recently, pushing the development of large-scale models capable of producing realistic videos with coherent motion. Due to memory constraints, these models typically generate short video segments that are then combined into long videos. The merging process poses a significant challenge, as it requires ensuring smooth transitions and overall consistency. In this paper, we introduce Anchored Diffusion, a novel method for synthesizing relatively long and seamless videos. We extend Diffusion Transformers (DiTs) to incorporate temporal information, creating our sequence-DiT (sDiT) model for generating short video segments. Unlike previous works, we train our model on video sequences with random non-uniform temporal spacing and incorporate temporal information via external guidance, increasing flexibility and allowing it to capture both short and long-term relationships. Furthermore, during inference, we leverage the transformer architecture to modify the diffusion process, generating a batch of non-uniform sequences anchored to a common frame, ensuring consistency regardless of temporal distance. To demonstrate our method, we focus on face reenactment, the task of creating a video from a source image that replicates the facial expressions and movements from a driving video. Through comprehensive experiments, we show our approach outperforms current techniques in producing longer consistent high-quality videos while offering editing capabilities.

Zero-Shot Image Compression with Diffusion-Based Posterior Sampling

Diffusion models dominate the field of image generation, however they have yet to make major breakthroughs in the field of image compression. Indeed, while pre-trained diffusion models have been successfully adapted to a wide variety of downstream tasks, existing work in diffusion-based image compression require task specific model training, which can be both cumbersome and limiting. This work addresses this gap by harnessing the image prior learned by existing pre-trained diffusion models for solving the task of lossy image compression. This enables the use of the wide variety of publicly-available models, and avoids the need for training or fine-tuning. Our method, PSC (Posterior Sampling-based Compression), utilizes zero-shot diffusion-based posterior samplers. It does so through a novel sequential process inspired by the active acquisition technique "Adasense" to accumulate informative measurements of the image. This strategy minimizes uncertainty in the reconstructed image and allows for construction of an image-adaptive transform coordinated between both the encoder and decoder. PSC offers a progressive compression scheme that is both practical and simple to implement. Despite minimal tuning, and a simple quantization and entropy coding, PSC achieves competitive results compared to established methods, paving the way for further exploration of pre-trained diffusion models and posterior samplers for image compression.

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.

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

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.

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 super-resolution algorithms.

Uncertainty-Aware PPG-2-ECG for Enhanced Cardiovascular Diagnosis using Diffusion Models

Analyzing the cardiovascular system condition via Electrocardiography (ECG) is a common and highly effective approach, and it has been practiced and perfected over many decades. ECG sensing is non-invasive and relatively easy to acquire, and yet it is still cumbersome for holter monitoring tests that may span over hours and even days. A possible alternative in this context is Photoplethysmography (PPG): An optically-based signal that measures blood volume fluctuations, as typically sensed by conventional ``wearable devices''. While PPG presents clear advantages in acquisition, convenience, and cost-effectiveness, ECG provides more comprehensive information, allowing for a more precise detection of heart conditions. This implies that a conversion from PPG to ECG, as recently discussed in the literature, inherently involves an unavoidable level of uncertainty. In this paper we introduce a novel methodology for addressing the PPG-2-ECG conversion, and offer an enhanced classification of cardiovascular conditions using the given PPG, all while taking into account the uncertainties arising from the conversion process. We provide a mathematical justification for our proposed computational approach, and present empirical studies demonstrating its superior performance compared to state-of-the-art baseline methods.

Early Time Classification with Accumulated Accuracy Gap Control

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.

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.