Diffusion Models: A Comprehensive Survey of Methods and Applications

Motivation

• Diffusion models [112] have emerged as state-of-the-art deep generative models and broken GANs’ dominance in image synthesis [60] [112].Their applications span robust machine learning [23] [33] [145] [310], computational chemistry [5] [134] [170], and medical image reconstruction [31] [47] [48] [49] [53] [204] [332].Source: §1 · pp. 3, 5

Survey scope

• The survey addresses rapidly expanding research that can obscure major trends by providing a comprehensive overview, categorization of approaches, and highlights of key advances.It aims to support both new and experienced researchers.Source: §1 · p. 5

Foundations

• The foundations section presents DDPMs [112], SGMs, and Score SDEs [142] under a shared noise-perturbation and denoising principle.It explains their connections and how the formulations can be reduced to one another.Source: §1 · p. 5

Taxonomy and model connections

• The survey taxonomy covers efficient sampling, improved likelihood estimation, and structured data methods for relational, permutation/rotationally invariant, and manifold data, while examining connections to VAEs [157], GANs, and normalizing flows.Source: §1 · p. 5

Applications and outlook

• The applications review covers computer vision, natural language process, temporal data modeling, multi-modal learning, robust learning, and interdisciplinary applications.For each task, it defines the problem, explains how diffusion models address it, summarizes prior work, and concludes with future directions.Source: §1 · p. 5

2 FOUNDATIONS OF DIFFUSION MODELS

• Diffusion models progressively perturb data with noise and learn to reverse that process for sample generation.The survey presents DDPMs, SGMs, and Score SDEs as the predominant formulations and discusses their connections.Source: §2 · p. 5

2.3 Stochastic Differential Equations (Score SDEs)

• The section introduces Score SDEs as one of the three predominant diffusion-model formulations, alongside DDPMs and SGMs.The supplied passage identifies Score SDEs but does not provide further formulation-specific details in this section part.Source: §2 · p. 5

2.1 Denoising Diffusion Probabilistic Models (DDPMs)

• DDPMs transform data toward a tractable Gaussian prior with a hand-designed forward Markov chain, then generate samples by iteratively applying a learnable reverse chain from noise.The reverse chain is trained by maximizing the variational lower bound, whose independent terms can be efficiently estimated with Monte Carlo sampling and stochastic optimization.Source: §2.1 · pp. 5–6

2.2 Score-Based Generative Models (SGMs)

• DDPM and SGM training objectives are equivalent when 𝝐𝜃(x,𝑡) = −𝜎𝑡s𝜃(x,𝑡), linking noise prediction to score estimation.SGMs perturb data with intensifying Gaussian noise, estimate scores across noise levels using noise-conditional networks, and decouple training from sampling.Source: §2.2 · p. 8
• SGMs can improve sampling efficiency through generalized high-order score matching, while Langevin dynamics converges to valid samples from the data distribution as step size approaches zero and iterations approach infinity.Their training–sampling decoupling permits multiple sampling techniques, including Langevin Monte Carlo, stochastic differential equations, and ordinary differential equations.Source: §2.2 · pp. 8–9, §2.3 · p. 9

2.3 Stochastic Differential Equations (Score SDEs)

• Score SDEs generalize DDPMs and SGMs to continuous time, modeling noise perturbation and denoising with SDEs and estimated score functions.The forward processes of DDPMs and SGMs are discretizations of the SDE formulation.Source: §2.3 · p. 9
• The reverse-time SDE converts noise to data, while the probability-flow ODE has trajectories with the same marginal densities as the reverse-time SDE.Both trajectories can therefore sample from the same data distribution.Source: §2.3 · pp. 9–10
• Once the time-dependent score ∇x log q_t(x) is known, samples can be generated by numerically solving either the reverse-time SDE or probability-flow ODE.Available approaches include numerical SDE and ODE solvers, annealed Langevin dynamics, and predictor-corrector methods [137] [142] [190] [377].Source: §2.3 · p. 10
• Later diffusion-model research focuses on faster sampling, more accurate likelihood and density estimation, and data with special structures such as permutation invariance, manifolds, and discrete values.The survey organizes these directions in Sections 3–5 and categorizes diffusion models in Table 1.Source: §2.3 · p. 10

3.1 Learning-Free Sampling

• Learning-free samplers reduce discretization steps and errors in reverse-time SDEs or probability-flow ODEs, whose sampling costs scale with the number of time steps.DDPM generation can be viewed as a reverse-time SDE discretization, motivating faster numerical schemes.Source: §3.1 · p. 10, §3.1.1 · p. 10

3.1.1 SDE Solvers.

• SDE solvers include Langevin-based methods, adaptive-step schemes, predictor-corrector sampling, and reverse diffusion, with correct marginals or improved speed and quality under stated conditions.ALD produces correct samples when Langevin dynamics reaches equilibrium at every noise level; reverse diffusion slightly outperforms DDPM for VP-SDEs, while correctors improve efficiency over additional predictors.Source: §3.1.1 · pp. 10–12
• Adding a Langevin Monte Carlo corrector is more efficient than using an additional predictor, while a Langevin-like churn step that adds and removes noise achieves new state-of-the-art sample quality on CIFAR-10 and ImageNet-64.Source: §3.1.1 · p. 12

3.1.2 ODE solvers.

• ODE solvers converge faster than stochastic SDE solvers but may slightly reduce quality; Heun’s 2nd-order method matches or exceeds Euler quality with fewer steps.Customized exponential-integrator methods exploit the semi-linear probability-flow ODE and can generate high-quality samples in 10 to 20 iterations.Source: §3.1.2 · pp. 12–13

3.2 Learning-Based Sampling

• Learning-based sampling selects partial or reverse-process steps through optimization, accelerating generation at the expense of slight sample-quality degradation.Unlike learning-free methods’ handcrafted steps, these methods optimize learning objectives to select sampling steps.Source: §3.2 · p. 13

3.2.1 Optimized Discretization.

• Optimized discretization selects K DDPM time steps by maximizing training objectives or directly optimizing KID [22] when the variational bound does not track sample quality.Differentiable Diffusion Sampler Search addresses the mismatch by optimizing KID with reparameterization and gradient rematerialization.Source: §3.2.1 · p. 13

3.2.2 Truncated Diffusion.

• Additional learning-based accelerators train a second-order solver head on a first-order score network or truncate the forward and reverse diffusion processes.Truncation begins by halting forward diffusion after only a few steps before starting the reverse process [201, 387].Source: §3.2.1 · p. 14, §3.2.2 · p. 14
• Truncated diffusion efficiently samples from a non-Gaussian reverse process by diffusing samples from pretrained variational autoencoders [157] or generative adversarial networks.Source: §3.2.2 · p. 14

3.2.3 Knowledge Distillation.

• Progressive Distillation distills the full process into a sampler requiring half as many steps by matching DDIM inputs and outputs, although repeated reduction can lower sample quality.Further efficiency improvements use new diffusion-model parameterizations and weighting schemes.Source: §3.2.3 · p. 14

4 DIFFUSION MODELS WITH IMPROVED LIKELIHOOD

• Likelihood-improvement methods target potentially suboptimal diffusion-model log-likelihoods caused by a non-tight variational lower bound [155].Source: §4 · p. 14

4.1 Noise Schedule Optimization

• Noise schedule optimization can maximize the VLB and improve log-likelihoods [155, 216], while schedules sharing endpoint signal-to-noise ratios affect only Monte Carlo estimator variance.iDDPM demonstrates that a cosine noise schedule can improve log-likelihoods.Source: §4.1 · pp. 14–15

4.3 Exact Likelihood Computation

• Likelihood computation uses the probability-flow ODE and computable variational lower bounds, while ScoreFlows are introduced to reduce the cost of directly maximizing p_ode [120].Source: §4.3 · p. 16

5.1 Discrete Data

• Discrete diffusion replaces Gaussian perturbations with random walks, masking, absorbing-state, or discretized-Gaussian kernels, while MMaDA [351] improves complex discrete-sequence modeling using cross-modal information.Continuous-time discrete diffusion can provide efficient samplers and theoretical error analysis relative to the true data distribution.Source: §5.1 · p. 17

5.2 Data with Invariant Structures

• Diffusion models can preserve graph permutation invariance and molecular rotation and translation invariance by using equivariant networks, kernels, and invariant priors.Xu et al. (2022) show that invariant priors and equivariant transition kernels guarantee invariant generated distributions.Source: §5.2 · p. 18

5.3 Data with Manifold Structures

• Manifold-structured data motivate diffusion models categorized by whether the manifold is known or learned, enabling modeling on lower-dimensional intrinsic spaces.Examples include climate and Earth data on spheres and learned latent spaces produced by autoencoders.Source: §5.3 · p. 18

5.3.1 Known Manifolds.

• Known-manifold methods extend score-based diffusion to compact Riemannian manifolds such as spheres and toruses, using intrinsic geodesic or extrinsic variational formulations.RSGM [56] uses geodesic random walks and generalized denoising score matching, whereas RDM [119] uses a variational lower bound and an embedded Euclidean representation.Source: §5.3.1 · pp. 18–19

5.3.2 Learned Manifolds.

• Learned-manifold methods condense data into a lower-dimensional autoencoder manifold before training diffusion models; LSGM jointly combines the VAE evidence lower bound with score matching, enabling faster sampling and discrete-data management.Source: §5.3.2 · p. 19

6 CONNECTIONS WITH OTHER GENERATIVE MODELS

• Diffusion models are combined with other generative models to promote their capabilities through complementary planning, latent representations, adversarial training, and flow-based transformations.The integrated algorithms are summarized in Table 2 and illustrated schematically in Fig. 3.Source: §6 · p. 19, Table 2 · p. 20, Figure 3 · p. 21

6.1 Large Language Models and Connections with Diffusion Models

• RPG uses multimodal-LLM vision-language priors to reason about spatial layouts, achieving state-of-the-art compositional synthesis for diffusion-based generation and editing.LLMs also support compositional layouts, image-editing datasets, temporal prompt decomposition, multimodal discrete diffusion, and high-level action-policy guidance.Source: §6.1 · p. 20

6.2 Variational Autoencoders and Connections with Diffusion Models

• Diffusion models connect to VAEs as hierarchical latent-variable models: DDPM uses a fixed forward encoder and shared reverse decoder, while score-based diffusion approaches the continuous-depth VAE limit.Latent score-based models further interpret ELBO optimization as a tractable score-matching objective in latent diffusion.Source: §6.2 · pp. 21–22

6.3 Generative Adversarial Networks and Connections with Diffusion Models

• GAN–diffusion hybrids inject adaptively scheduled diffusion noise into discriminators, use conditional GAN denoisers for larger diffusion steps, or adversarially enforce authentic manifold structures.These designs address GAN training instability or diffusion sampling slowness while preserving structural fidelity.Source: §6.3 · p. 22

6.4 Normalizing Flows and Connections with Diffusion Models

• DiffFlow combines flow and diffusion models to produce sharper boundaries and more general distributions with fewer discretization steps than diffusion probabilistic models.INDM applies normalizing-flow pre-encoding before latent diffusion and uses nonlinear diffusion to improve likelihood and sampling speed.Source: §6.4 · p. 23
• Consistency Flow Matching [359] bridges consistency and flow-matching models by defining straight flows whose velocity values remain consistent across starting times.It explicitly enforces self-consistency in the velocity field and connects different times to the same endpoint.Source: §6.4 · p. 23

6.5 Autoregressive Models and Connections with Diffusion Models

• Autoregressive Diffusion Models [117] include order-agnostic autoregressive and discrete diffusion models as special cases while enabling parallel generation at test time.Their diffusion-like training objective supports arbitrary-generation tasks without requiring the sequential network calls typical of autoregressive models.Source: §6.5 · p. 24
• Randomized smoothing improves the sample quality of autoregressive models while retaining reasonable likelihoods by learning a smoothed distribution and subsequently denoising it.The smoothing distribution can use Gaussian or Laplacian kernels, followed by gradient-based denoising or a conditional autoregressive model.Source: §6.5 · p. 24

6.6 Energy-based Models and Connections with Diffusion Models

• Constrained score models, or energy-based models, can perform as well as unconstrained models when they use a comparable model structure.However, high-dimensional EBMs face expensive MCMC-based likelihood learning and instability when MCMC fails to converge.Source: §6.6 · p. 24
• Diffusion recovery likelihood [83] makes EBM learning more tractable by training a sequence of EBMs on conditional noisy-data distributions in the reverse diffusion process.Conditional distributions are easier to sample than marginal distributions, making recovery likelihood preferable for this construction.Source: §6.6 · pp. 24–25

7 APPLICATIONS OF DIFFUSION MODELS

• Diffusion-model applications are organized into six categories, with Table 3 summarizing how diffusion models are used across these tasks.The categories are computer vision, natural language processing, temporal data modeling, multi-modal learning, robust learning, and interdisciplinary applications.Source: §7 · p. 25, Table 3 · p. 25

7.1 Unconditional and Conditional Diffusion Models

• Conditional diffusion models support application-level control, while unconditional generation is used to explore generative-model performance limits; diffusion models also offer strong quality, diversity, and controllability.The survey focuses on conditional diffusion models with labels, classifiers, texts, images, semantic maps, and graphs as conditioning forms.Source: §7.1 · p. 25

7.1.1 Conditioning Mechanisms in Diffusion Models

• Four main conditioning mechanisms are identified: concatenation, gradient-based guidance, cross-attention, and adaptive layer normalization.These mechanisms respectively combine conditions with denoising targets, inject task-related gradients during sampling, pass messages between guidance and diffusion targets, or regress normalization parameters from time embeddings and conditions.Source: §7.1.1 · pp. 25–26

7.1.2 Diffusion with DPO/RLHF

• IterComp [382] iteratively aligns diffusion models with composition-aware preferences and outperforms three other conditional diffusion approaches while achieving the best inference efficiency.It uses preferences from a gallery of six powerful open-source diffusion models, and the comparison is shown in Fig. 4.Source: §7.1.2 · p. 26

7.1.3 Condition Diffusion on Labels and Classifiers

• When labels are limited, self-guided diffusion, dual pseudo training, classifier guidance, and classifier-free score combination provide strategies for conditioning and balancing sample quality against diversity.SGGM conditions on self-produced hierarchical labels, while You et al. (2023) [365] use dual pseudo training; Dhariwal and Nichol [60] use an auxiliary classifier, and Ho and Salimans [114] combine conditional and unconditional scores.Source: §7.1.3 · p. 26

7.1.4 Condition Diffusion on Texts, Images, and Semantic Maps

• Text, image, and semantic-map conditioning expands diffusion applications to NLP, image-to-image translation, latent diffusion, text-to-image generation, image editing, and compositional generation.Pre-alignment [245] [346] strengthens guidance across modalities, while unCLIP [245] and ConPreDiff use CLIP latents to align image and text semantics.Source: §7.1.4 · p. 26

7.1.5 Condition Diffusion on Graphs

• Graph conditioning is difficult because graphs contain complex node relations, but SGDiff [346] enables scene-graph-to-image generation, while other models generate 2D graphs or 3D molecules from graph representations.SGDiff [346] uses masked contrastive pre-training; Graphusion conditions on latent graph clusters, and BindDM [122], IPDiff, and IRDiff condition on 3D protein graphs.Source: §7.1.5 · p. 28

7.2.1 Image Super Resolution, Inpainting, Restoration, Translation, and Editing

• Diffusion models tackle image restoration tasks including super-resolution, inpainting, and translation; SR3 uses DDPM with iterative denoising, CDM [113] uses multiple diffusion models, and latent-space diffusion shifts the process using pre-trained autoencoders.The Latent Diffusion Model streamlines training and sampling processes.Source: §7.2.1 · p. 28

7.2.1 Image Super Resolution, Inpainting, Restoration, Translation, and Editing.

• DDRM [144] uses a pre-trained denoising diffusion model to solve linear inverse problems, demonstrating versatility across super-resolution, deblurring, inpainting, and colorization.These applications are evaluated on several image datasets under varying measurement noise.Source: §7.2.1 · p. 29

7.2.2 Semantic Segmentation.

• DDPM-learned representations support few-shot semantic segmentation and outperform VDVAE [44] and ALAE, while DDeP yields promising label-efficient results.ODISE further targets open-vocabulary segmentation using an implicit captioner to exploit large-scale text-to-image diffusion models.Source: §7.2.2 · p. 29

7.2.3 Video Generation.

• Diffusion models improve video generation through arbitrary-subset frame sampling in FDM [108] and autoregressive residual prediction in RVD [361].FDM uses a specialized architecture, whereas RVD generates future frames by adding stochastic residuals to deterministic next-frame predictions.Source: §7.2.3 · pp. 29–30

7.2.4 Generating Data from Diffusion Models.

• Diffusion models generate task-specific training data, including few-shot classification augmentations, hierarchical distribution-aware expansions, and world-instructed image-editing datasets.EditWorld [355] combines pretrained LLMs and diffusion models to synthesize examples reflecting real-world and virtual-media knowledge and dynamics.Source: §7.2.4 · p. 30

7.2.5 Point Cloud Completion and Generation.

• Diffusion methods reconstruct incomplete point clouds by modeling particles thermodynamically, combining denoising with point-voxel representations, or refining conditional coarse completions.These methods target missing parts caused by partial observation or self-occlusion and support downstream 3D reconstruction and scene understanding.Source: §7.2.5 · pp. 30–31

7.2.6 Anomaly Detection.

• AnoDDPM reconstructs healthy image approximations, while DDPM-CD uses pretrained DDPM representations to detect changes in remote-sensing images.Diffusion-based approaches may outperform adversarial alternatives through effective sampling and stable training on smaller datasets.Source: §7.2.6 · pp. 31–32

7.3 Natural Language Generation

• Diffusion language models support character-level text generation [9] and complex control via continuous diffusion [176], whose denoising steps produce hierarchical continuous latent representations that enable gradient-based methods.Source: §7.3 · p. 32

7.4.1 Text-to-Image Generation.

• Imagen [260] performs well against VQ-GAN+CLIP [52], Latent Diffusion Models [190], and DALL-E 2 [245] on its text-to-image benchmark.The model combines text conditioning with diffusion-based image generation and includes a comprehensive benchmark for evaluation.Source: §7.4.1 · p. 33
• RPG unifies text-guided image generation and image editing in a closed-loop fashion, outperforms SOTA methods such as SDXL [235] and DALL-E 3, and generalizes across MLLM architectures and diffusion backbones.Source: §7.4.1 · p. 34

7.4.2 Scene Graph-to-Image Generation.

• Scene graph-to-image diffusion uses continuous semantically aligned SG embeddings, enabling SGDiff [346] to express complex relationships better than non-diffusion and diffusion methods.SGDiff [346] applies masked contrastive pre-training for global and local semantic alignment, while scarce paired SG-image data remains an open limitation.Source: §7.4.2 · p. 37

7.4.3 Text-to-3D Generation.

• Diffusion-based text-to-3D methods synthesize 3D content through text-to-image diffusion, cascaded low- and high-resolution stages, reference images, and distributional optimization.One framework enables users to create controllable and high-quality 3D objects.Source: §7.4.3 · pp. 37–38

7.4.4 Text-to-Motion Generation.

• Text-to-motion diffusion models adapt transformer architectures to human pose sequences, supporting geometric regularization, variable-length motion, free-form text, and frame-wise or joint-wise editing.MDM [294] uses classifier-free diffusion with geometric losses, while FLAME [152] handles variable-length motions and editable motion parts.Source: §7.4.4 · p. 38

7.4.5 Text-to-Video Generation.

• Text-to-video methods extend text-to-image diffusion through factorized, cascaded, one-shot, and zero-shot designs that target high-definition output, reduced data requirements, and temporal consistency.Make-A-Video [275] bypasses paired text-video data with a joint text-image prior; Tune-A-Video [322] reduces large-scale video training; Text2Video-Zero [149] uses latent motion and cross-frame attention; FateZero [239] targets temporal-consistent video editing.Source: §7.4.5 · p. 38
• Text-to-video editing methods fuse DDIM inversion and generation attention maps to preserve motion and structural consistency, while ContextDiff incorporates cross-modal context through forward-backward consistency.ContextDiff uses interactions between text conditions and video samples in the forward and reverse processes.Source: §7.4.5 · p. 38
• Fixed-size video training datasets limit many text-to-video diffusion models to short clips, causing substantial quality degradation for longer videos.Vlogger [394] conditions on masked input frames, while StreamingT2V [109] uses ControlNet-like conditioning for autoregressive generation.Source: §7.4.5 · p. 40
• VideoTetris generates superior-quality compositional videos and high-quality long videos aligned with compositional prompts while maintaining the best performance in qualitative comparisons.It uses spatio-temporal compositional diffusion, new video preprocessing, and Reference Frame Attention to improve motion dynamics and prompt semantics during autoregressive long-video generation.Source: §7.4.5 · p. 40

7.4.6 Text-to-Audio Generation.

• Text-to-audio generation includes Grad-TTS, which uses a score-based decoder and Monotonic Alignment Search to align diffusion outputs with text.Grad-TTS2 [153] adaptively improves Grad-TTS, while Diffsound [340] uses a non-autoregressive discrete diffusion decoder that predicts and iteratively refines mel-spectrogram tokens.Source: §7.4.6 · p. 40
• EdiTTS [290] refines a coarsely modified mel-spectrogram prior with a score-based text-to-speech model, while ProDiff [121] directly predicts clean data during denoising.These approaches modify the diffusion process for text-to-speech refinement and parameterization.Source: §7.4.6 · p. 40

7.5.1 Time Series Imputation.

• Diffusion models address time-series imputation by exploiting temporal correlations, with CSDI using self-supervised training and outperforming previous methods on real-world datasets.SSSD [3] combines conditional diffusion with structured state-space models to capture long-term dependencies and performs well in imputation and forecasting.Source: §7.5.1 · p. 40

7.5.2 Time Series Forecasting.

• RATD introduces retrieval-augmented time-series diffusion, using historical-series references as guidance during denoising to better utilize the dataset for complex forecasting.The historical series is retrieved and concatenated with noise as the model input, while the references guide denoising.Source: §7.5.2 · p. 41, Figure 17 · p. 41

7.5.3 Waveform Signal Processing.

• WaveGrad [39] conditionally generates waveforms by iteratively refining Gaussian noise, trading inference speed for sample quality through the number of refinement steps.DiffWave [160] provides a non-autoregressive diffusion model for conditional or unconditional waveform generation and produces high-fidelity audio.Source: §7.5.3 · p. 41

7.6 Robust Learning

• Diffusion-based robust learning purifies adversarial examples by adding forward noise and reconstructing clean images, while ADP purifies attacks in only a few steps.PGD [23] introduces model-agnostic stochastic diffusion-based preprocessing intended to produce high-quality denoised outcomes.Source: §7.6 · pp. 41–42

7.7.1 Drug Design and Life Science.

• Diffusion methods enhance molecule or protein generation through torsion-angle diffusion [134] and GeoDiff’s equivariant Markov kernels, which produce invariant distributions while preserving equivariance.A diffusion-based 3D antibody design framework models both sequence and structure and supports jointly generating sequence-structure and designing CDRs.Source: §7.7.1 · pp. 42–43
• IPDiff beats previous diffusion-based and autoregressive models on binding-related metrics and molecular properties for structure-based drug design.It incorporates pocket-ligand interactions into both forward and reverse processes through prior-conditioning and prior-shifting mechanisms.Source: §7.7.1 · p. 42

7.7.2 Material Design.

• CDVAE applies a noise-conditional score network to material design while incorporating stability and permutation, translation, rotation, and periodic invariances.The supplied passage identifies these invariances as properties used by the model.Source: §7.7.2 · p. 43

7.7.3 Medical Image Reconstruction.

• Score-based diffusion models reconstruct CT and MRI images by combining learned priors with observed measurements and alternating numerical SDE solving with data-consistency steps.These methods address medical-image reconstruction as an inverse problem.Source: §7.7.3 · pp. 43–44

7.7.3 Medical Image Reconstruction

• In medical image reconstruction, reverse diffusion is guided by observed k-space signals using a coarse-to-fine sampling algorithm for efficient sampling.Source: §7.7.3 · p. 44

• Diffusion-model research is still in its early stages, leaving substantial potential for theoretical and empirical improvement.Source: §8 · p. 44
• Key research directions include efficient sampling and improved likelihood estimation.Source: §8 · p. 44
• Future work will address special data structures, interfaces with other generative models, and tailoring diffusion models to diverse applications.Source: §8 · p. 44

Revisiting Assumptions.

• Finite-time forward diffusion may fail to completely remove information from data or render it equivalent to the prior distribution.Complete information removal is unachievable in finite time.Source: Revisiting Assumptions · p. 44
• Choosing when to halt forward noising is important for balancing sampling efficiency and sample quality [79].Source: Revisiting Assumptions · p. 44
• Schrödinger bridges and optimal transport [55] [271] [280] offer alternative formulations that can converge to a specified prior in finite time.Source: Revisiting Assumptions · p. 44

• Diffusion models rival GANs in most applications without relying on adversarial training.Source: Theoretical Understanding · p. 44
• Theory should identify how diffusion models differ from variational autoencoders, energy-based models, and autoregressive models, and when those differences make them effective.Source: Theoretical Understanding · p. 44
• A central goal is to explain diffusion models’ excellent sample quality and top likelihood while developing systematic guidance for choosing hyperparameters.Source: Theoretical Understanding · p. 44

Latent Representations

• Compared with variational autoencoders or generative adversarial networks, diffusion models provide less effective latent-space representations [133].Their latent spaces may not learn representation schemes well.Source: Latent Representations · p. 44
• Because diffusion-model latent spaces often match data dimensionality, they hinder sampling efficiency and make semantic data manipulation difficult.These limitations arise alongside weakly learned representations.Source: Latent Representations · p. 44

• Generative pre-training underpins GPT-1/2/3/4 [222] and Visual ChatGPT [320], which show strong generation and emergent abilities.These systems use Large Language Models and Visual Foundation Models.Source: AIGC and Diffusion Foundation Models · p. 44
• Transferring decoder-only generative pre-training to diffusion models enables evaluation of generation at scale and analysis of diffusion foundation-model emergent abilities.Source: AIGC and Diffusion Foundation Models · p. 44
• Specialized diffusion foundation models are emerging across domains, including MMaDA [351] for multimodal generation with emergent cross-modal reasoning.Source: AIGC and Diffusion Foundation Models · pp. 44–45
• TraceRL [311] adapts diffusion foundation models for reinforcement learning by generating coherent action sequences while preserving foundation-model scalability.Source: AIGC and Diffusion Foundation Models · p. 45
• Combining LLMs with diffusion models is a promising direction [355] for AIGC systems that leverage complementary generative strengths [182].Source: AIGC and Diffusion Foundation Models · p. 45

• The survey introduces three foundational diffusion-model formulations: DDPMs, SGMs, and Score SDEs.Source: §9 · p. 45
• It organizes improvements around sampling efficiency, likelihood maximization, and techniques for data with special structures.Source: §9 · p. 45
• The survey examines connections with other generative models and outlines potential benefits of combining them.Source: §9 · p. 45
• Applications across six domains demonstrate the wide-ranging potential of diffusion models.Source: §9 · p. 45
• The conclusion outlines possible avenues for future research.Source: §9 · p. 45