The paper establishes a reverse-time quantum diffusion framework that generates complex quantum ensembles from simple distributions by deriving and learning a feedback Hamiltonian from forward trajectory data.
super hub Canonical reference
Score-Based Generative Modeling through Stochastic Differential Equations
Canonical reference. 76% of citing Pith papers cite this work as background.
540
Pith papers citing it
191
external citations · Pith
Background
76% of classified citations
abstract
Creating noise from data is easy; creating data from noise is generative modeling. We present a stochastic differential equation (SDE) that smoothly transforms a complex data distribution to a known prior distribution by slowly injecting noise, and a corresponding reverse-time SDE that transforms the prior distribution back into the data distribution by slowly removing the noise. Crucially, the reverse-time SDE depends only on the time-dependent gradient field (\aka, score) of the perturbed data distribution. By leveraging advances in score-based generative modeling, we can accurately estimate these scores with neural networks, and use numerical SDE solvers to generate samples. We show that this framework encapsulates previous approaches in score-based generative modeling and diffusion probabilistic modeling, allowing for new sampling procedures and new modeling capabilities. In particular, we introduce a predictor-corrector framework to correct errors in the evolution of the discretized reverse-time SDE. We also derive an equivalent neural ODE that samples from the same distribution as the SDE, but additionally enables exact likelihood computation, and improved sampling efficiency. In addition, we provide a new way to solve inverse problems with score-based models, as demonstrated with experiments on class-conditional generation, image inpainting, and colorization. Combined with multiple architectural improvements, we achieve record-breaking performance for unconditional image generation on CIFAR-10 with an Inception score of 9.89 and FID of 2.20, a competitive likelihood of 2.99 bits/dim, and demonstrate high fidelity generation of 1024 x 1024 images for the first time from a score-based generative model.
hub tools
citation-role summary
background 73
method 17
baseline 3
other 1
citation-polarity summary
claims ledger
- abstract Creating noise from data is easy; creating data from noise is generative modeling. We present a stochastic differential equation (SDE) that smoothly transforms a complex data distribution to a known prior distribution by slowly injecting noise, and a corresponding reverse-time SDE that transforms the prior distribution back into the data distribution by slowly removing the noise. Crucially, the reverse-time SDE depends only on the time-dependent gradient field (\aka, score) of the perturbed data distribution. By leveraging advances in score-based generative modeling, we can accurately estimate
authors
co-cited works
representative citing papers
WavTTS is the first raw-waveform diffusion TTS model using DiT flow matching and multi-scale mel supervision that approaches SOTA latent zero-shot performance while beating prior end-to-end models.
Flux Matching generalizes score-based generative modeling by using a weaker objective that admits infinitely many non-conservative vector fields with the data as stationary distribution, enabling new design choices beyond traditional score matching.
A-CODE presents a fully atomic one-stage multimodal diffusion model for protein co-design that claims superior unconditional generation performance over prior one- and two-stage models plus a tenfold success-rate gain on hard binder-design tasks.
FMRG reformulates guidance as deterministic optimal control, deriving a single-trajectory method using the flow map that matches or exceeds baselines on reward-guided generation and inverse problems with 3 NFEs at text-to-image scale.
Quotient-space diffusion models generate correct symmetric distributions by removing redundancy on the quotient space, simplifying learning and improving results on small molecules and proteins under SE(3) symmetry.
The García-Pintos feedback Hamiltonian equals the score function of the quantum trajectory distribution, linking quantum feedback to diffusion-model reversal.
Diffusion sampling from d-dimensional distributions requires at least ~sqrt(d) adaptive score queries when score estimates have polynomial accuracy.
OP-GRPO is the first off-policy GRPO method for flow-matching models that reuses trajectories via replay buffer and importance sampling corrections, matching on-policy performance with 34.2% of the training steps.
Generative diffusion and flow models are constructed to remain exactly on the Lorentz-invariant massless N-particle phase space manifold during sampling for particle physics applications.
ASTRA reframes transition-state search as guided diffusion inference that samples the isodensity surface between metastable basins and converges to first-order saddles via score differences and physical forces.
MF-PID turns independent diffusion samples into mean-field interacting agents, proving that quadratic interactions yield exact linear mean interpolation and delivering 19-24% energy savings in demand-response control.
Föllmer processes are variationally optimal among generative diffusions because they minimize the impact of drift estimation error on path-space KL divergence, rendering different interpolation schedules statistically equivalent.
Flow-GRPO is the first online RL method for flow matching models, raising GenEval accuracy from 63% to 95% and text-rendering accuracy from 59% to 92% with little reward hacking.
LLaDA is a scalable diffusion-based language model that matches autoregressive LLMs like LLaMA3 8B on tasks and surpasses GPT-4o on reversal poem completion.
DDIMs construct non-Markovian diffusion processes that share DDPM training objectives but allow much faster reverse sampling, demonstrated empirically at 10-50x wall-clock speedup.
A two-stage algorithm learns a coordinate chart and a low-rank tensor source for a linear PDE, reducing supervised learning on manifolds to independent 1D integrals with automatic intrinsic dimension discovery.
Set diffusion factorizes likelihood over arbitrary token sets and uses a set-causal diffusion architecture to support KV caching and any-order decoding, yielding improved speed-quality tradeoffs versus prior diffusion LMs.
Proposes diffeomorphic optimization for manifold-constrained problems in generative models via flow maps, with Lie-group extensions for protein design showing metric improvements.
Flow-Map GRPO uses anchored stochastic flow map composition to enable GRPO-based RL alignment of deterministic few-step flow-map generators while preserving their marginal paths.
Introduces a Bridge latent interface that maps mismatched student latents into teacher space, enabling distillation from modern diffusion teachers to compact one-step students and raising SD 1.5 HPSv3 from 5.4 to 9.4 while keeping one-step speed.
FlexiSLM is the first spoken language model supporting dynamic and controllable frame rates on speech input and output, outperforming fixed-rate 7B models at high quality and enabling faster inference at lower rates like 6.25 Hz.
ReMatch corrects train-test residual distribution mismatch in probabilistic downscaling via optimal transport in low-dimensional PCA space, reducing under-dispersion and improving SSR and CRPS on HRRR-ERA5 wind data.
Hybrid simulation and non-Euclidean elasticity theory demonstrate that clathrin coats develop adaptive rigidity and memory during growth, producing flat, stalled, or closed outcomes through two energy-landscape gates and matching experiments without fitted parameters.
citing papers explorer
-
Generating quantum ensembles via reverse-time quantum diffusions
The paper establishes a reverse-time quantum diffusion framework that generates complex quantum ensembles from simple distributions by deriving and learning a feedback Hamiltonian from forward trajectory data.
-
WavTTS: Towards High-Quality Zero-Shot TTS via Direct Raw Waveform Modeling
WavTTS is the first raw-waveform diffusion TTS model using DiT flow matching and multi-scale mel supervision that approaches SOTA latent zero-shot performance while beating prior end-to-end models.
-
Generative Modeling with Flux Matching
Flux Matching generalizes score-based generative modeling by using a weaker objective that admits infinitely many non-conservative vector fields with the data as stationary distribution, enabling new design choices beyond traditional score matching.
-
A-CODE: Fully Atomic Protein Co-Design with Unified Multimodal Diffusion
A-CODE presents a fully atomic one-stage multimodal diffusion model for protein co-design that claims superior unconditional generation performance over prior one- and two-stage models plus a tenfold success-rate gain on hard binder-design tasks.
-
How to Guide Your Flow: Few-Step Alignment via Flow Map Reward Guidance
FMRG reformulates guidance as deterministic optimal control, deriving a single-trajectory method using the flow map that matches or exceeds baselines on reward-guided generation and inverse problems with 3 NFEs at text-to-image scale.
-
Quotient-Space Diffusion Models
Quotient-space diffusion models generate correct symmetric distributions by removing redundancy on the quotient space, simplifying learning and improving results on small molecules and proteins under SE(3) symmetry.
-
The Feedback Hamiltonian is the Score Function: A Diffusion-Model Framework for Quantum Trajectory Reversal
The García-Pintos feedback Hamiltonian equals the score function of the quantum trajectory distribution, linking quantum feedback to diffusion-model reversal.
-
Query Lower Bounds for Diffusion Sampling
Diffusion sampling from d-dimensional distributions requires at least ~sqrt(d) adaptive score queries when score estimates have polynomial accuracy.
-
OP-GRPO: Efficient Off-Policy GRPO for Flow-Matching Models
OP-GRPO is the first off-policy GRPO method for flow-matching models that reuses trajectories via replay buffer and importance sampling corrections, matching on-policy performance with 34.2% of the training steps.
-
Generative models on phase space
Generative diffusion and flow models are constructed to remain exactly on the Lorentz-invariant massless N-particle phase space manifold during sampling for particle physics applications.
-
A Priori Sampling of Transition States with Guided Diffusion
ASTRA reframes transition-state search as guided diffusion inference that samples the isodensity surface between metastable basins and converges to first-order saddles via score differences and physical forces.
-
Mean-Field Path-Integral Diffusion: From Samples to Interacting Agents
MF-PID turns independent diffusion samples into mean-field interacting agents, proving that quadratic interactions yield exact linear mean interpolation and delivering 19-24% energy savings in demand-response control.
-
Variational Optimality of F\"ollmer Processes in Generative Diffusions
Föllmer processes are variationally optimal among generative diffusions because they minimize the impact of drift estimation error on path-space KL divergence, rendering different interpolation schedules statistically equivalent.
-
Flow-GRPO: Training Flow Matching Models via Online RL
Flow-GRPO is the first online RL method for flow matching models, raising GenEval accuracy from 63% to 95% and text-rendering accuracy from 59% to 92% with little reward hacking.
-
Large Language Diffusion Models
LLaDA is a scalable diffusion-based language model that matches autoregressive LLMs like LLaMA3 8B on tasks and surpasses GPT-4o on reversal poem completion.
-
Denoising Diffusion Implicit Models
DDIMs construct non-Markovian diffusion processes that share DDPM training objectives but allow much faster reverse sampling, demonstrated empirically at 10-50x wall-clock speedup.
-
Intrinsic Green's Learning: Supervised Learning on Manifolds via Inverse PDE
A two-stage algorithm learns a coordinate chart and a low-rank tensor source for a linear PDE, reducing supervised learning on manifolds to independent 1D integrals with automatic intrinsic dimension discovery.
-
Set Diffusion: Interpolating Token Orderings Between Autoregression and Diffusion for Fast and Flexible Decoding
Set diffusion factorizes likelihood over arbitrary token sets and uses a set-causal diffusion architecture to support KV caching and any-order decoding, yielding improved speed-quality tradeoffs versus prior diffusion LMs.
-
Diffeomorphic Optimization
Proposes diffeomorphic optimization for manifold-constrained problems in generative models via flow maps, with Lie-group extensions for protein design showing metric improvements.
-
Flow-Map GRPO: Reinforcement Learning for Few-Step Flow-Map Generators via Anchored Stochastic Composition
Flow-Map GRPO uses anchored stochastic flow map composition to enable GRPO-based RL alignment of deterministic few-step flow-map generators while preserving their marginal paths.
-
Cross-Space Distillation: Teaching One-Step Students with Modern Diffusion Teachers
Introduces a Bridge latent interface that maps mismatched student latents into teacher space, enabling distillation from modern diffusion teachers to compact one-step students and raising SD 1.5 HPSv3 from 5.4 to 9.4 while keeping one-step speed.
-
FlexiSLM: A Dynamic and Controllable Frame Rate Spoken Language Model
FlexiSLM is the first spoken language model supporting dynamic and controllable frame rates on speech input and output, outperforming fixed-rate 7B models at high quality and enabling faster inference at lower rates like 6.25 Hz.
-
Mind the Residual Gap: Probabilistic Downscaling under Real-World Bias
ReMatch corrects train-test residual distribution mismatch in probabilistic downscaling via optimal transport in low-dimensional PCA space, reducing under-dispersion and improving SSR and CRPS on HRRR-ERA5 wind data.
-
Pathway variability, coat stiffening and mechanical adaptation during clathrin-mediated endocytosis
Hybrid simulation and non-Euclidean elasticity theory demonstrate that clathrin coats develop adaptive rigidity and memory during growth, producing flat, stalled, or closed outcomes through two energy-landscape gates and matching experiments without fitted parameters.
-
A Distributionally Robust Framework for Learned Reconstructions in Inverse Problems
Introduces structured DRO for learned inverse problem reconstructions with ambiguity sets aligned to the forward operator, yielding explicit dual representations and a worst-case bound that induces Tikhonov regularization on the operator Lipschitz constant.
-
CORDEX-ML-Bench: A Benchmark for Data-Driven Regional Climate Downscaling -Experiment Design and Overview
CORDEX-ML-Bench benchmarks 40 ML models for climate downscaling and finds generative models outperform deterministic ones on precipitation while historically trained models underestimate future climate signals.
-
Probing Probability Geometry with Schwinger--Dyson Identities: Score Mismatch, Fisher Information, and Configurational Temperature
Schwinger-Dyson identities are given a geometric reading in which their violations are controlled by the score-mismatch field δs = ∇ log(Q/P_eq), yielding a bound on Fisher information and a tomographic view of probability distortion.
-
Focusing on What Matters: Saliency-Harnessing Accurate Routing for Diffusion MoE
SharpMoE is a plug-and-play post-training method that uses clean latent features and a trajectory routing loss to enable accurate saliency-based routing in diffusion MoE models for improved visual generation.
-
When Does Synthetic Data Augmentation Improve Score-Based Imbalanced Classification?
Synthetic minority augmentation improves threshold-integrated and optimized classification metrics only under model misspecification by correcting ranking errors, while providing no fundamental benefit beyond possible variance reduction under well-specified score models.
-
Quasi-Monte Carlo for SDE Simulation: Error Analysis and Dimensionality Reduction
QMC applied to Euler-Maruyama yields faster sampling-error decay than Monte Carlo, and the new MSTG method based on exact simulation achieves super-exponential truncation-error decay that sharply reduces integration dimension.
-
Safe Few-Step Generation via Velocity Editing
VESFlow edits the learned velocity field of flow matching models via a safe-conditional posterior to produce safe images in 4 sampling steps, with an optional risk filter and VESFlow+ variant that also repels from unsafe directions.
-
Variance-Tilted Diffusion Models for Diverse Sampling
Derives an interacting-particle diffusion sampler via Doob h-transform that targets batches with high empirical variance under a linear feature map.
-
Patched Flow Matching: Generative Wall-Pressure Reconstruction Beyond Training-Domain Scales from Sparse Sensors
Patched Flow Matching reconstructs full-resolution wall-pressure fields on domains four times larger than training data from 0.25% sensor coverage by fusing short-domain DNS patch priors with sparse measurements via training-free posterior sampling.
-
Diffusion-Driven State Space Models
DDSSM replaces Gaussian transitions in SSMs with diffusion models to jointly train autoencoders and diffusion on sequential data, outperforming standard deep SSMs on simulated multimodal time series.
-
$\Omega$: Operator-based Mixture Ensemble for Generative Assimilation
Ω is a generative assimilation method that learns residual discrepancies from ensemble data using a conditional Gaussian baseline, then reconstructs full non-Gaussian posteriors via Gaussian mixtures and annealed Langevin sampling.
-
Frequency-Aware Flow Matching for Continuous and Consistent Robotic Action Generation
FAFM performs flow matching in the frequency domain using DCT on action sequences to produce continuous temporally consistent robotic actions with a Sobolev-style smoothness regularizer.
-
Timage: A Generative Text-in-Image Paradigm for Fine-Tuning Vision-Language Models
Timage generates text query overlays on images via Constrained Schrödinger Bridge to boost fine-grained spatial reasoning in vision-language models, outperforming larger systems on VMCBench with a 7B backbone.
-
The Reward Was in Your Data All Along: Correcting Flow Matching with Discriminator-Guided RL
DRL trains a discriminator on data versus base-model samples in pretrained representation space and uses its logit as reward in KL-regularized RL, cutting guidance-free FID from 9.38 to 2.62 on SiT and similar gains on other backbones.
-
Fast Computation of Free-Support Wasserstein Medians
Direct fixed-weight solver for free-support Wasserstein medians relocates atoms using OT barycentric projections and inverse-distance weights, achieving monotone descent on smoothed objectives with fewer subproblems than nested Weiszfeld baselines.
-
Volterra Generative Models
Volterra generative models add path-dependent fractional noise to score-based diffusion via Markovian lifts with error bounds, showing improved MNIST generation and a stability sampler for larger approximations.
-
Ambient Diffusion Policy: Imitation Learning from Suboptimal Data in Robotics
Ambient Diffusion Policy enables better imitation learning from suboptimal robot data by leveraging spectral properties to restrict data usage to specific diffusion times.
-
Conditional Model-Adequacy Tests for Spectral Uncertainty Claims in Lattice QCD
Introduces target-wise model-adequacy tests on Euclidean-admissible mock correlators to evaluate coverage properties of reported spectral uncertainties in lattice QCD reconstructions.
-
The Power of Test-Time Training for Approximate Sampling
Establishes a quadratic lower bound on query complexity for sampling from large classes of distributions given approximate density oracles, answers an open question on optimality of random walks, and shows circumvention for bounded classes as an abstraction of TTT.
-
Rethinking 3D Shape Generation: Diffusion over Superquadrics
Diffusion for 3D shapes is moved from dense geometry to compact superquadric parameter sets, cutting state size to roughly 7 KB per shape and enabling faster generation plus new editing capabilities.
-
Synthetic but Not Realistic: The Evaluation Challenge in Generative Modelling for Structured Electronic Medical Records
Generative models for synthetic EMRs match marginal distributions but fail to preserve subgroup structure, effect estimates, and dependency structure simultaneously on the PRIME-CVD cohort.
-
Improving Bayesian Optimization via Training-Aware Conditional Diffusion Models
Conditional diffusion models trained with BO-aware strategies approximate the optimum distribution, enabling a Diffusion-based Mode Seeking acquisition function with a sub-optimality guarantee that outperforms baselines in experiments.
-
SMC-ITA: Sequential Monte Carlo Inference-Time Alignment for Video-to-Audio Generation
SMC-ITA applies sequential Monte Carlo resampling with lookahead-based multi-dimensional cross-modal rewards to improve inference-time alignment in video-to-audio generation, reporting 55.67% DeSync reduction and gains in IB-score and audio quality over baselines.
-
Complexity-Balanced Diffusion Splitting
CBS partitions the diffusion timeline into segments of equal approximation burden via Dirichlet energy and trajectory acceleration monitors estimated by an auxiliary model, yielding higher synthesis quality at fixed per-step cost across SiT, JiT and UNet backbones.
-
Parallel Jacobi Decoding for Fast Autoregressive Image Generation
Parallel Jacobi Decoding accelerates autoregressive image models 4.8x-6.4x by using 2D spatial draft expansion and adjusted attention masks while keeping generation quality competitive.
-
Correcting Neural Operator Spectral Bias via Diffusion Posterior Sampling with Sparse Observations
FreqNO-DPS corrects neural operator spectral bias in 3D elastic wavefield prediction by frequency-dependent guidance in diffusion posterior sampling conditioned on sparse observations, achieving near-zero bias at 2-5% sensor coverage.