Diffusion Model Research Articles

Study on the UV FEL single-shot damage threshold of an Au thin film.

The damage threshold of an Au-coated flat mirror, one of the reflective optics installed on the FEL-2 beamline of the Dalian Coherent Light Source, China, upon far-UV free-electron laser irradiation is evaluated. The surface of the coating is characterized by profilometer and optical microscope. A theoretical approach of the phenomenon is also presented, by application of conventional single-pulse damage threshold calculations, a one-dimensional thermal diffusion model, as well as finite-element analysis with ANSYS.

DiffPhys: Enhancing Signal-to-Noise Ratio in Remote Photoplethysmography Signal Using a Diffusion Model Approach.

Remote photoplethysmography (rPPG) is an emerging non-contact method for monitoring cardiovascular health based on facial videos. The quality of the captured videos largely determines the efficacy of rPPG in this application. Traditional rPPG techniques, while effective for heart rate (HR) estimation, often produce signals with an inadequate signal-to-noise ratio (SNR) for reliable vital sign measurement due to artifacts like head motion and measurement noise. Another pivotal factor is the overlooking of the inherent properties of signals generated by rPPG (rPPG-signals). To address these limitations, we introduce DiffPhys, a novel deep generative model particularly designed to enhance the SNR of rPPG-signals. DiffPhys leverages the conditional diffusion model to learn the distribution of rPPG-signals and uses a refined reverse process to generate rPPG-signals with a higher SNR. Experimental results demonstrate that DiffPhys elevates the SNR of rPPG-signals across within-database and cross-database scenarios, facilitating the extraction of cardiovascular metrics such as HR and HRV with greater precision. This enhancement allows for more accurate monitoring of health conditions in non-clinical settings.

Experimental and modeling of potassium diclofenac uptake on activated carbon.

The presence of pharmaceuticals in wastewater resulting from human activities has driven researchers to explore effective treatment methods such as adsorption using activated carbon (AC). While AC shows promise as an adsorbent, further studies are essential to comprehend its entire interaction with pharmaceuticals. This article investigates the adsorption of potassium diclofenac (PD) onto AC using experimental and modeling approaches. Batch adsorption studies coupled with Fourier transform infrared spectroscopy (FTIR) were employed to clarify the adsorption mechanism of PD on AC. Various kinetic and isotherm adsorption models were applied to analyze the adsorbent-adsorbate interaction. The kinetics were best described by Avrami's fractional order (AFO) nonlinear model. Also, the intraparticle diffusion (IP) model reveals a three-stage adsorption process. The experimental equilibrium data fitted well with the three-parameter nonlinear Liu model, indicating a maximum adsorption capacity (Qmax) of 88.45mgg-1 and suggesting monolayer or multilayer adsorption. Thermodynamic analysis showed favorable adsorption (ΔG° < 0), with an enthalpy change (ΔH° = -30.85kJmol-1) characteristic of physisorption involving hydrogen bonds and π-π interactions. The adsorption mechanism was attributed to forming a double layer (adsorbate-adsorbent and adsorbate-adsorbate).

Adsorption study of CO2/CH4 and CO2/N2 binary mixtures on titanosilicates ETS-10 and SrETS-10; industrial application aspects

Despite the outstanding features of the titanosilicate ETS-10 and some studies done on CO2 adsorption so far, there is a lack of coherent information to evaluate its potential industrial application in CO2 separation from natural gas and flue gas. In this work, ETS-10 and SrETS-10 were synthesized and characterized by PXRD, SEM, DTA, EDX, and BET. Pure gas adsorption isotherms of CO2, CH4, and N2 at 298 K were obtained by the constant-volume method. The obtained adsorption data were fitted with Langmuir and UNILAN isotherm models. The CO2/CH4 selectivity (yCO2 = 0.05) predicted by Ideal Adsorption Solution Theory (IAST) was 67.54 and 35.65 for ETS-10 and SrETS-10, respectively, while the CO2/N2 selectivity (yCO2 = 0.04) was 94.64 and 99.94. The Pseudo-Nth-Order (PNO) and micropore diffusion model were used to evaluate the CO2 adsorption kinetics and diffusivity of the adsorbents. The results showed that both ETS-10 and SrETS-10 exhibited fast kinetics for CO2 adsorption, but SrETS-10 had a slightly smaller diffusion coefficient (DC/rC2 = 0.01494 and 0.01458 s−1 for ETS-10 and SrETS-10, respectively) resulting in a slower adsorption rate than ETS-10. The regenerability of ETS-10 and SrETS-10 was studied and it was found that for ETS-10 about 79.07% and 96.32% of the capacity can be regenerated by applying vacuum and heating, respectively and also 79.67% of the SrETS-10 capacity can also be regenerated by applying vacuum. From the results of this work with an approach of industrial application, it was concluded that ETS-10 and SrETS-10 can be used in a combined PSA and TSA process for CO2 separation.

Front stability of infinitely steep travelling waves in population biology

Reaction–diffusion models are often used to describe biological invasion, where populations of individuals that undergo random motility and proliferation lead to moving fronts. Many reaction–diffusion models of biological invasion are extensions of the well–known Fisher–Kolmogorov–Petrovskii–Piskunov model that describes the spatiotemporal evolution of a 1D population density, u(x,t) , as a result of linear diffusion with flux J=−∂u/∂x , and logistic growth source term, S=u(1−u) . In 2020 Fadai introduced a new reaction–diffusion model of biological invasion with a nonlinear degenerate diffusive flux, J=−u∂u/∂x , and the model was formulated as a moving boundary problem on 0<x<L(t) , with u(L(t),t)=0 and dL(t)/dt=−κu∂u/∂x at x=L(t) (Fadai and Simpson 2020 J. Phys. A: Math. Theor. 53 095601). Fadai’s model leads to travelling wave solutions with infinitely steep, well–defined fronts at the moving boundary, and the model has the mathematical advantage of being analytically tractable in certain parameter limits. In this work we consider the stability of the travelling wave solutions presented by Fadai. We provide general insight by first presenting two key extensions of Fadai’s model by considering: (i) generalised nonlinear degenerate diffusion with flux J=−um∂u/∂x for some constant m > 0; and, (ii) solutions describing both biological invasion with dL(t)/dt>0 , and biological recession with dL(t)/dt<0 . After establishing the existence of travelling wave solutions for these two extensions, our main contribution is to consider stability of the travelling wave solutions by introducing a lateral perturbation of the travelling wavefront. Full 2D time–dependent level–set numerical solutions indicate that invasive travelling waves are stable to small amplitude lateral perturbations, whereas receding travelling waves are unstable. These preliminary numerical observations are corroborated through a linear stability analysis that gives more formal insight into short time growth/decay of wavefront perturbation amplitude. Julia–based software, including level–set algorithms, is available on Github to replicate all results in this study.

SOFT MODIFICATION AND FUNCTIONALIZATION OF LIGNOCELLULOSIC BIOMASS USED AS A LOW-COST EFFICIENT BIOSORBENT TO REMOVE BASIC FUCHSINE FROM AQUEOUS SOLUTION

This study proposes a new modification of lignocellulosic biomass based on apricot kernel shells with composite activation KI/KOH and functionalized with a tolerant material (MgO) powder. Apricot kernel shells (NAK), modified apricot kernel shells (MAK) and doped apricot kernel shells (DAK) obtained were characterized using various methods, such as infrared spectroscopy (FTIR), scanning electron microscopy coupled with energy-dispersive X-ray spectroscopy (SEM-EDX), thermogravimetric analysis (TGA), X-ray diffraction (XRD), and point of zero charge (pHpzc). The adsorbents were also evaluated in batch adsorption, using basic fuchsine dye (BF) to determine the performance and specific capacity of the adsorption process. The results showed that only 90 min and 0.1 g of DAK or MAK are sufficient to remove 93% and 91%, respectively, of basic fuchsine from aqueous solutions with a concentration of 20 mg/L in a volume of 100 mL. The MAK and DAK adsorbents can be reused for 5 cycles before their yield decreases below 50%, without requiring complex regeneration procedures, only drying for 4 h at 105°C. The evolution of adsorption was analyzed under different parameters, such as contact time, initial dose of adsorbent, initial dye concentration, initial pH, and temperature. The kinetic adsorption models indicate that the pseudo-second-order model was more suitable than the pseudo-first-order and intraparticle diffusion models for describing the adsorption process. The equilibrium adsorption data of BF were better fitted by the Langmuir isotherm, compared to the Freundlich and Temkin isotherms.

Interactive Character Control with Auto-Regressive Motion Diffusion Models

Real-time character control is an essential component for interactive experiences, with a broad range of applications, including physics simulations, video games, and virtual reality. The success of diffusion models for image synthesis has led to the use of these models for motion synthesis. However, the majority of these motion diffusion models are primarily designed for offline applications, where space-time models are used to synthesize an entire sequence of frames simultaneously with a pre-specified length. To enable real-time motion synthesis with diffusion model that allows time-varying controls, we propose A-MDM (Auto-regressive Motion Diffusion Model). Our conditional diffusion model takes an initial pose as input, and auto-regressively generates successive motion frames conditioned on the previous frame. Despite its streamlined network architecture, which uses simple MLPs, our framework is capable of generating diverse, long-horizon, and high-fidelity motion sequences. Furthermore, we introduce a suite of techniques for incorporating interactive controls into A-MDM, such as task-oriented sampling, in-painting, and hierarchical reinforcement learning (See Figure 1). These techniques enable a pre-trained A-MDM to be efficiently adapted for a variety of new downstream tasks. We conduct a comprehensive suite of experiments to demonstrate the effectiveness of A-MDM, and compare its performance against state-of-the-art auto-regressive methods.

Denoising diffusion post-processing for low-light image enhancement

Low-light image enhancement (LLIE) techniques attempt to increase the visibility of images captured in low-light scenarios. However, as a result of enhancement, a variety of image degradations such as noise and color bias are revealed. Furthermore, each particular LLIE approach may introduce a different form of flaw within its enhanced results. To combat these image degradations, post-processing denoisers have widely been used, which often yield oversmoothed results lacking detail. We propose using a diffusion model as a post-processing approach, and we introduce Low-light Post-processing Diffusion Model (LPDM) in order to model the conditional distribution between under-exposed and normally-exposed images. We apply LPDM in a manner which avoids the computationally expensive generative reverse process of typical diffusion models, and post-process images in one pass through LPDM. Extensive experiments demonstrate that our approach outperforms competing post-processing denoisers by increasing the perceptual quality of enhanced low-light images on a variety of challenging low-light datasets. Source code is available at https://github.com/savvaki/LPDM.

EASI-Tex: Edge-Aware Mesh Texturing from Single Image

We present a novel approach for single-image mesh texturing , which employs a diffusion model with judicious conditioning to seamlessly transfer an object's texture from a single RGB image to a given 3D mesh object. We do not assume that the two objects belong to the same category, and even if they do, there can be significant discrepancies in their geometry and part proportions. Our method aims to rectify the discrepancies by conditioning a pre-trained Stable Diffusion generator with edges describing the mesh through ControlNet, and features extracted from the input image using IP-Adapter to generate textures that respect the underlying geometry of the mesh and the input texture without any optimization or training. We also introduce Image Inversion , a novel technique to quickly personalize the diffusion model for a single concept using a single image , for cases where the pre-trained IP-Adapter falls short in capturing all the details from the input image faithfully. Experimental results demonstrate the efficiency and effectiveness of our edge-aware single-image mesh texturing approach, coined EASI-Tex, in preserving the details of the input texture on diverse 3D objects, while respecting their geometry. Code : https://github.com/sairajk/easi-tex

Analogist: Out-of-the-box Visual In-Context Learning with Image Diffusion Model

Visual In-Context Learning (ICL) has emerged as a promising research area due to its capability to accomplish various tasks with limited example pairs through analogical reasoning. However, training-based visual ICL has limitations in its ability to generalize to unseen tasks and requires the collection of a diverse task dataset. On the other hand, existing methods in the inference-based visual ICL category solely rely on textual prompts, which fail to capture fine-grained contextual information from given examples and can be time-consuming when converting from images to text prompts. To address these challenges, we propose Analogist, a novel inference-based visual ICL approach that exploits both visual and textual prompting techniques using a text-to-image diffusion model pretrained for image inpainting. For visual prompting, we propose a self-attention cloning (SAC) method to guide the fine-grained structural-level analogy between image examples. For textual prompting, we leverage GPT-4V's visual reasoning capability to efficiently generate text prompts and introduce a cross-attention masking (CAM) operation to enhance the accuracy of semantic-level analogy guided by text prompts. Our method is out-of-the-box and does not require fine-tuning or optimization. It is also generic and flexible, enabling a wide range of visual tasks to be performed in an in-context manner. Extensive experiments demonstrate the superiority of our method over existing approaches, both qualitatively and quantitatively. Our project webpage is available at https://analogist2d.github.io.

Transparent Image Layer Diffusion using Latent Transparency

We present an approach enabling large-scale pretrained latent diffusion models to generate transparent images. The method allows generation of single transparent images or of multiple transparent layers. The method learns a "latent transparency" that encodes alpha channel transparency into the latent manifold of a pretrained latent diffusion model. It preserves the production-ready quality of the large diffusion model by regulating the added transparency as a latent offset with minimal changes to the original latent distribution of the pretrained model. In this way, any latent diffusion model can be converted into a transparent image generator by finetuning it with the adjusted latent space. We train the model with 1M transparent image layer pairs collected using a human-in-the-loop collection scheme. We show that latent transparency can be applied to different open source image generators, or be adapted to various conditional control systems to achieve applications like foreground/background-conditioned layer generation, joint layer generation, structural control of layer contents, etc. A user study finds that in most cases (97%) users prefer our natively generated transparent content over previous ad-hoc solutions such as generating and then matting. Users also report the quality of our generated transparent images is comparable to real commercial transparent assets like Adobe Stock.

BrepGen: A B-rep Generative Diffusion Model with Structured Latent Geometry

This paper presents BrepGen , a diffusion-based generative approach that directly outputs a Boundary representation (B-rep) Computer-Aided Design (CAD) model. BrepGen represents a B-rep model as a novel structured latent geometry in a hierarchical tree. With the root node representing a whole CAD solid, each element of a B-rep model (i.e., a face, an edge, or a vertex) progressively turns into a child-node from top to bottom. B-rep geometry information goes into the nodes as the global bounding box of each primitive along with a latent code describing the local geometric shape. The B-rep topology information is implicitly represented by node duplication. When two faces share an edge, the edge curve will appear twice in the tree, and a T-junction vertex with three incident edges appears six times in the tree with identical node features. Starting from the root and progressing to the leaf, BrepGen employs Transformer-based diffusion models to sequentially denoise node features while duplicated nodes are detected and merged, recovering the B-Rep topology information. Extensive experiments show that BrepGen advances the task of CAD B-rep generation, surpassing existing methods on various benchmarks. Results on our newly collected furniture dataset further showcase its exceptional capability in generating complicated geometry. While previous methods were limited to generating simple prismatic shapes, BrepGen incorporates free-form and doubly-curved surfaces for the first time. Additional applications of BrepGen include CAD autocomplete and design interpolation. The code, pretrained models, and dataset are available at https://github.com/samxuxiang/BrepGen.

SketchDream: Sketch-based Text-To-3D Generation and Editing

Existing text-based 3D generation methods generate attractive results but lack detailed geometry control. Sketches, known for their conciseness and expressiveness, have contributed to intuitive 3D modeling but are confined to producing texture-less mesh models within predefined categories. Integrating sketch and text simultaneously for 3D generation promises enhanced control over geometry and appearance but faces challenges from 2D-to-3D translation ambiguity and multi-modal condition integration. Moreover, further editing of 3D models in arbitrary views will give users more freedom to customize their models. However, it is difficult to achieve high generation quality, preserve unedited regions, and manage proper interactions between shape components. To solve the above issues, we propose a text-driven 3D content generation and editing method, SketchDream, which supports NeRF generation from given hand-drawn sketches and achieves free-view sketch-based local editing. To tackle the 2D-to-3D ambiguity challenge, we introduce a sketch-based multi-view image generation diffusion model, which leverages depth guidance to establish spatial correspondence. A 3D ControlNet with a 3D attention module is utilized to control multi-view images and ensure their 3D consistency. To support local editing, we further propose a coarse-to-fine editing approach: the coarse phase analyzes component interactions and provides 3D masks to label edited regions, while the fine stage generates realistic results with refined details by local enhancement. Extensive experiments validate that our method generates higher-quality results compared with a combination of 2D ControlNet and image-to-3D generation techniques and achieves detailed control compared with existing diffusion-based 3D editing approaches.

DreamMat: High-quality PBR Material Generation with Geometry- and Light-aware Diffusion Models

Recent advancements in 2D diffusion models allow appearance generation on untextured raw meshes. These methods create RGB textures by distilling a 2D diffusion model, which often contains unwanted baked-in shading effects and results in unrealistic rendering effects in the downstream applications. Generating Physically Based Rendering (PBR) materials instead of just RGB textures would be a promising solution. However, directly distilling the PBR material parameters from 2D diffusion models still suffers from incorrect material decomposition, such as baked-in shading effects in albedo. We introduce DreamMat , an innovative approach to resolve the aforementioned problem, to generate high-quality PBR materials from text descriptions. We find out that the main reason for the incorrect material distillation is that large-scale 2D diffusion models are only trained to generate final shading colors, resulting in insufficient constraints on material decomposition during distillation. To tackle this problem, we first finetune a new light-aware 2D diffusion model to condition on a given lighting environment and generate the shading results on this specific lighting condition. Then, by applying the same environment lights in the material distillation, DreamMat can generate high-quality PBR materials that are not only consistent with the given geometry but also free from any baked-in shading effects in albedo. Extensive experiments demonstrate that the materials produced through our methods exhibit greater visual appeal to users and achieve significantly superior rendering quality compared to baseline methods, which are preferable for downstream tasks such as game and film production.

Quantitative Volumetric Analysis of Retinal Ischemia with an Oxygen Diffusion Model and OCT Angiography

PurposeRetinal ischemia is a major feature of diabetic retinopathy (DR). Traditional nonperfused areas measured by optical coherence tomography angiography (OCTA) measure blood supply but not ischemia. We propose a novel 3-dimensional (3D) quantitative method to derive ischemia measurements from OCTA data. DesignCross-sectional study. ParticipantsWe acquired 223 macular OCTA volumes from 33 healthy eyes, 33 diabetic eyes without retinopathy, 7 eyes with non-referable DR, 17 eyes with referable but non-vision-threatening DR, and 133 eyes with vision-threatening DR. MethodsEach eye was scanned using a spectral-domain OCTA system (Avanti RTVue-XR, Visionix/Optovue, Inc) with 1.6 mm scan depth in a 3 × 3-mm region (640 × 304 × 304 voxels) centered on the fovea. For each scanned OCTA volume, a custom algorithm removed flow projection artifacts. We then enhanced, binarized, and skeletonized the vasculature in each OCTA volume and generated a 3D oxygen tension map using a zero-order kinetics oxygen diffusion model. Each volume was scaled to the average retina thickness in healthy controls after foveal registration and flattening of the Bruch membrane. Finally, we extracted 3D ischemia maps by comparison with a reference map established from scans of healthy eyes using the same processing. To assess the ability of the ischemia maps to grade DR severity, we constructed receiver-operating characteristic (ROC) curves for diagnosing diabetes, referable DR, and vision-threatening DR. Main outcome measuresSpearman correlation coefficient and area under ROC curve (AUC) were used to quantify the ability of the ischemia maps to DR. ResultsThe ischemia maps showed that the ischemic tissues were at or near pathologically non-perfused areas, but not the normally non-vascular tissue, such as the foveal avascular zone. We found multiple novel metrics, including inferred 3D-oxygen tension, ischemia index, and ischemic volume ratio, were strongly correlated with DR severity. The AUCs of ischemia index measured were 0.95 for diabetes, 0.89 for DR, 0.88 for referable DR, and 0.85 for vision threatening DR. ConclusionsA quantitative method to infer 3D oxygen tension and ischemia using OCTA in diabetic eyes can identify ischemic tissue that are more specific to pathologic changes in DR.

One Noise to Rule Them All: Learning a Unified Model of Spatially-Varying Noise Patterns

Procedural noise is a fundamental component of computer graphics pipelines, offering a flexible way to generate textures that exhibit "natural" random variation. Many different types of noise exist, each produced by a separate algorithm. In this paper, we present a single generative model which can learn to generate multiple types of noise as well as blend between them. In addition, it is capable of producing spatially-varying noise blends despite not having access to such data for training. These features are enabled by training a denoising diffusion model using a novel combination of data augmentation and network conditioning techniques. Like procedural noise generators, the model's behavior is controllable via interpretable parameters plus a source of randomness. We use our model to produce a variety of visually compelling noise textures. We also present an application of our model to improving inverse procedural material design; using our model in place of fixed-type noise nodes in a procedural material graph results in higher-fidelity material reconstructions without needing to know the type of noise in advance. Open-sourced materials can be found at https://armanmaesumi.github.io/onenoise/

DiffPoseTalk: Speech-Driven Stylistic 3D Facial Animation and Head Pose Generation via Diffusion Models

The generation of stylistic 3D facial animations driven by speech presents a significant challenge as it requires learning a many-to-many mapping between speech, style, and the corresponding natural facial motion. However, existing methods either employ a deterministic model for speech-to-motion mapping or encode the style using a one-hot encoding scheme. Notably, the one-hot encoding approach fails to capture the complexity of the style and thus limits generalization ability. In this paper, we propose DiffPoseTalk, a generative framework based on the diffusion model combined with a style encoder that extracts style embeddings from short reference videos. During inference, we employ classifier-free guidance to guide the generation process based on the speech and style. In particular, our style includes the generation of head poses, thereby enhancing user perception. Additionally, we address the shortage of scanned 3D talking face data by training our model on reconstructed 3DMM parameters from a high-quality, in-the-wild audio-visual dataset. Extensive experiments and user study demonstrate that our approach outperforms state-of-the-art methods. The code and dataset are at https://diffposetalk.github.io.

CLAY: A Controllable Large-scale Generative Model for Creating High-quality 3D Assets

In the realm of digital creativity, our potential to craft intricate 3D worlds from imagination is often hampered by the limitations of existing digital tools, which demand extensive expertise and efforts. To narrow this disparity, we introduce CLAY, a 3D geometry and material generator designed to effortlessly transform human imagination into intricate 3D digital structures. CLAY supports classic text or image inputs as well as 3D-aware controls from diverse primitives (multi-view images, voxels, bounding boxes, point clouds, implicit representations, etc). At its core is a large-scale generative model composed of a multi-resolution Variational Autoencoder (VAE) and a minimalistic latent Diffusion Transformer (DiT), to extract rich 3D priors directly from a diverse range of 3D geometries. Specifically, it adopts neural fields to represent continuous and complete surfaces and uses a geometry generative module with pure transformer blocks in latent space. We present a progressive training scheme to train CLAY on an ultra large 3D model dataset obtained through a carefully designed processing pipeline, resulting in a 3D native geometry generator with 1.5 billion parameters. For appearance generation, CLAY sets out to produce physically-based rendering (PBR) textures by employing a multi-view material diffusion model that can generate 2K resolution textures with diffuse, roughness, and metallic modalities. We demonstrate using CLAY for a range of controllable 3D asset creations, from sketchy conceptual designs to production ready assets with intricate details. Even first time users can easily use CLAY to bring their vivid 3D imaginations to life, unleashing unlimited creativity.

CharacterGen: Efficient 3D Character Generation from Single Images with Multi-View Pose Canonicalization

BNRist, Department of Computer Science and Technology, Tsinghua University, China In the field of digital content creation, generating high-quality 3D characters from single images is challenging, especially given the complexities of various body poses and the issues of self-occlusion and pose ambiguity. In this paper, we present CharacterGen, a framework developed to efficiently generate 3D characters. CharacterGen introduces a streamlined generation pipeline along with an image-conditioned multi-view diffusion model. This model effectively calibrates input poses to a canonical form while retaining key attributes of the input image, thereby addressing the challenges posed by diverse poses. A transformer-based, generalizable sparse-view reconstruction model is the other core component of our approach, facilitating the creation of detailed 3D models from multi-view images. We also adopt a texture-back-projection strategy to produce high-quality texture maps. Additionally, we have curated a dataset of anime characters, rendered in multiple poses and views, to train and evaluate our model. Our approach has been thoroughly evaluated through quantitative and qualitative experiments, showing its proficiency in generating 3D characters with high-quality shapes and textures, ready for downstream applications such as rigging and animation.

Neural‐network‐based regularization methods for inverse problems in imaging

AbstractThis review provides an introduction to—and overview of—the current state of the art in neural‐network based regularization methods for inverse problems in imaging. It aims to introduce readers with a solid knowledge in applied mathematics and a basic understanding of neural networks to different concepts of applying neural networks for regularizing inverse problems in imaging. Distinguishing features of this review are, among others, an easily accessible introduction to learned generators and learned priors, in particular diffusion models, for inverse problems, and a section focusing explicitly on existing results in function space analysis of neural‐network‐based approaches in this context.