Neural Flow Diffusion Models improve diffusion models by learning flexible forward processes.
problem Fixed forward processes in diffusion models complicate reverse processes and increase inference costs.
method Introduces NFDM, a framework supporting flexible forward processes and a novel parameterization technique.
result Demonstrates strong performance in likelihood estimation and learning generative dynamics.
The study examines how shallow neural nets converge to training samples or manifold points during diffusion.
problem Understanding when and how shallow neural nets converge to training samples or manifold points during diffusion.
method Analysis of shallow ReLU neural network denoisers trained with minimal ℓ 2 \ell^2 ℓ 2 norm, comparing score flow and diffusion flow. result Probability flow converges to training points, sums of training points, or manifold points, depending on the diffusion time scheduler.
Graph neural network using Beltrami flow for feature and topology evolution.
problem Efficient feature learning and topology evolution on graphs.
method Discretized Beltrami flow applied to graph neural networks with positional encodings.
result Achieves state-of-the-art results on various benchmarks.
Improved NPE with conditional diffusions and summary networks.
problem Approximating complex posterior distributions efficiently and accurately.
method Conditional diffusions coupled with high-capacity summary networks.
result Conditional diffusions offer improved stability, accuracy, and faster training times.
New method for estimating diffusion model densities without solving flows.
problem Estimating log densities from diffusion models efficiently.
method Monte Carlo path integral estimation, avoiding flow solving.
result Significantly more scalable and efficient density estimation.
Language Rectified Flow improves diffusion language generation by simplifying complex steps.
problem Complexity in diffusion language models limits their implementation in NLP applications.
method Reformulates probabilistic flow models to learn neural ODE models for efficient domain transfer.
result Consistently outperforms baselines on fine-grained control tasks and text editing.
New method learns diffusion transition density for Bayesian inference.
problem Bayesian inference on diffusions with inaccessible boundaries.
method Neural Galerkin framework to solve FP equation with Dirac mass.
result Approximates likelihood function for efficient posterior sampling.
This work combines recurrent models with diffusion for probabilistic time series forecasting.
problem Scalability and capturing high-dimensional distributions and cross-feature dependencies in time series forecasting.
method Combines recurrent neural networks' efficiency with diffusion models' probabilistic modeling, using stochastic interpolants and conditional generation.
result Offers scalable probabilistic time series forecasting methods.
Improved language generation with faster sampling speed.
problem Speed and coherence issues in autoregressive language models.
method Introduces Neural Flow Diffusion Models (NFDM) for discrete state spaces.
result Substantially reduces likelihood gap with autoregressive models.
DMVI uses diffusion models for efficient probabilistic inference in PPLs.
problem Efficient probabilistic inference in complex probabilistic programming languages.
method DMVI employs diffusion models as variational approximations to the posterior distribution, optimizing a bound on the marginal likelihood.
result DMVI produces more accurate posterior inferences than existing methods in PPLs with similar computational cost and less manual tuning.
Paper introduces new methods for modeling categorical data.
problem Training generative models on categorical data like text and segmentation.
method Argmax Flows and Multinomial Diffusion models.
result Models outperform existing methods in log-likelihood.
CTM improves diffusion model sampling quality with efficient ODE traversal.
problem Lack of natural trade-off between sample quality and speed in consistency models.
method CTM trains a neural network to output scores and traverse ODE trajectories efficiently.
result CTM achieves state-of-the-art FIDs and improves sample quality with increased computational budget.
This work interprets diffusion score matching using normalizing flows for better model training and evaluations.
problem Limitations of diffusion score matching when dealing with certain types of distributions.
method The approach involves interpreting the diffusion matrix using normalizing flows to provide better interpretation and usage of diffusion score matching.
result Diffusion score matching is equivalent to the original score matching evaluated in the transformed space defined by the normalizing flow.
New method uses diffusion models to solve inverse problems.
problem Solving ill-posed inverse problems with powerful priors.
method Formulate posterior sampling as a regularized Wasserstein gradient flow in latent space.
result Demonstrates improved performance on standard benchmarks.
Spatiotemporal forecasting has various applications in neuroscience, climate and transportation domain. Traffic forecasting is one canonical example of such learning task. The task is challenging due to (1) complex spatial dependency on road networks, (2) non-linear temporal dynamics with changing road conditions and (…
Flow Matching enables robust training of CNFs with various probability paths.
problem Training Continuous Normalizing Flows (CNFs) at large scales.
method Flow Matching (FM) is a simulation-free approach for training CNFs by regressing vector fields of conditional probability paths.
result Flow Matching with diffusion paths yields more robust and stable training compared to diffusion-based methods.
Existence of translating solutions shown for curve diffusion flow.
problem Existence of translating solutions for curve diffusion flow.
method Higher order curve shortening flow approach.
result Properly immersed translating solutions exist.
Efficiently solves inverse problems with diffusion and flow models in just a few steps.
problem Solving inverse problems like super-resolution, inpainting, or deblurring using diffusion or flow models.
method Conditional Conjugate Integrators framework that projects inverse problem dynamics into a more amenable space for sampling.
result Generates high-quality samples in as few as 5 conditional sampling steps, outperforming competing methods.
GLASS Flows improves flow and diffusion model performance by optimizing sampling efficiency.
problem Efficiency bottleneck in sampling Markov transitions for flow and diffusion models.
method Introduces GLASS Flows, a new sampling paradigm that simulates a 'flow matching model within a flow matching model' to sample Markov transitions efficiently.
result Eliminates the trade-off between stochastic evolution and efficiency in large-scale text-to-image models.
Novel estimator reduces diffusion model variance.
problem High variance in score function estimation for diffusion models.
method Uses nearest neighbour samples to estimate the score function.
result Significant decrease in variance, leading to improved model performance.
In deep latent Gaussian models, the latent variable is generated by a time-inhomogeneous Markov chain, where at each time step we pass the current state through a parametric nonlinear map, such as a feedforward neural net, and add a small independent Gaussian perturbation. This work considers the diffusion limit of suc…
Unified framework reduces NFEs for inverse problems.
problem High computational costs and degraded reconstruction quality in existing LDM-based inverse solvers.
method Consistency Regularised Gradient Flows for posterior sampling and prompt optimization.
result Significantly reduced computational cost with state-of-the-art performance.
Proposes LDIDPs for efficient sequential data generation from latent dynamical models.
problem Challenges in generating high-fidelity sequential samples from latent dynamical models.
method Utilizes implicit diffusion processes to sample from latent dynamical processes.
result Demonstrates accurate learning of dynamics and efficient generation of high-quality sequential data.
Review of diffusion models for SBI in non-ideal data scenarios.
problem Inference of parameters from complex simulation outputs with intractable likelihoods.
method Diffusion models for likelihood-free inference, addressing model misspecification, unstructured observations, and missing data.
result Improved robustness and efficiency in SBI methods for non-ideal data scenarios.
Study shows diffused interface flows to single diffused balls over time.
problem Volume-preserving mean curvature flow in Euclidean space.
method Diffused interface version, exponential convergence proof.
result Exponential convergence to single diffused balls.
Develops a smooth operator framework for analyzing neural network representations.
problem Analyzing the geometry of feedforward neural network representations.
method Introduces a smooth operator-theoretic approach based on diffusion Markov operators derived from feature clouds.
result Establishes a stable operator-geometric framework for tracking training, width, and perturbation stability.
iGNN tackles inverse graph prediction using invertible neural networks.
problem Inverse graph prediction problem in data analysis and machine learning.
method Developed invertible graph neural network (iGNN) to solve inverse prediction problem on graphs.
result iGNN model allows efficient generation from output labels and forward prediction.
Generative model improved using Liouville PDE-based sliced-Wasserstein flow.
problem Improving generative models for fair regression.
method Transformed sliced-Wasserstein flow into Liouville PDE-based formalism, handling density estimation with normalizing flows of neural ODE.
result Outperforms in convergence and fairness with reduced variance.
JKO-iFlow uses neural ODEs to improve generative models with reduced memory and training complexity.
problem Efficiently training deep generative models in high dimensions with reduced memory and training complexity.
method JKO scheme inspired neural ODE flow network with adaptive time reparameterization.
result JKO-iFlow achieves competitive performance compared to existing models at reduced computational and memory cost.
TFM trains Neural SDEs without backpropagation, improving clinical time series modeling.
problem Modeling irregularly sampled time series in medicine.
method Trajectory Flow Matching (TFM) using flow matching for generative modeling.
result TFM improves performance on clinical time series datasets.
Flow Matching for count data improves sample quality and efficiency.
problem Mapping between count distributions across batches or time points in high-dimensional count data.
method count-FM, a flow-matching framework based on a continuous-time birth-death process with local unit jumps.
result count-FM achieves better sample quality than representative baselines while using fewer parameters.
The paper justifies time-dependent loss reweighting schemes for flow matching and diffusion models.
problem Theoretical justification for time-dependent loss reweighting schemes in flow matching and diffusion models.
method Clarifies that the loss can depend on both time and state, and shows theoretical justification for time-dependent loss weighting schemes.
result Time-dependent loss weighting schemes are theoretically justified for Generator Matching and Edit Flows.
New diffusion models capture heavy-tailed distributions better.
problem Diffusion models struggle with rare or extreme events in heavy-tailed distributions.
method Repurposed diffusion framework using multivariate Student-t distributions, tailored perturbation kernel, and γ γ γ -divergence. result Our models generate rare and extreme events more effectively than standard diffusion models.
AdjointDEIS simplifies diffusion model optimization.
problem Optimizing diffusion models with respect to a differentiable metric.
method Novel bespoke ODE solvers for continuous adjoint equations.
result Continuous adjoint equations simplify to a simple ODE, improving efficiency.
A new deep learning method for option pricing in rough volatility models.
problem Efficient pricing of European options in high-dimensional rough volatility models.
method Time-stepping deep gradient flow method reformulating the option pricing PDE as an energy minimization problem.
result The method respects asymptotic behavior and known bounds for option prices.
Smooth convergence shown for curve diffusion flows.
problem Embeddedness and global existence of curves.
method Exponentially fast convergence established.
result Smooth convergence for curve diffusion flows.
Novel alignment framework for text-to-image generation using diffusion models and flow matching.
problem Improving text-to-image generation with minimal computational resources.
method Proposes a novel alignment framework that decomposes the score function into pre-trained score plus a conditional expectation of the reward.
result Achieves comparable performance to finetuning-based models with reduced computational cost.
LFM learns a sequence of smaller models to generate data from noise.
problem Learning continuous, invertible flows between distributions.
method Stepwise Local Flow Matching (LFM) model, matching diffusion processes up to time-step size.
result LFM achieves competitive generative performance compared to Flow Matching.
New error bounds for flow matching methods using deterministic sampling.
problem Improving the accuracy of flow matching methods for generating probability distributions.
method Derived error bounds for flow matching methods under deterministic sampling conditions.
result Presented error bounds for flow matching methods using L 2 L^2 L 2 loss and regularity conditions. Surface diffusion and mean curvature flows converge to stable critical sets in flat tori.
problem Stability of surface diffusion and mean curvature flows in flat tori.
method Existence and convergence of flows starting close to stable critical sets, proven for all times.
result Flows converge exponentially fast to stable critical sets in flat tori.
Classifies solitons for surface diffusion flow of graphs.
problem Classifying solitons for surface diffusion flow of graphs.
method Classifies solitons including equilibria, self-similar solutions, and travelling waves.
result Classified solitons for surface diffusion flow of entire graphs.
Survey of diffusion and optimal transport methods in machine learning.
problem Design and analysis of time-evolving probability distributions in machine learning.
method Switch from Eulerian to Lagrangian representation through vector fields.
result Both diffusion methods and optimal transport offer computational advantages.
Generative models tackle incompressible fluid flows by enforcing divergence-free constraints.
problem Simulating incompressible fluid flows with generative models.
method Score-based diffusion models with divergence-free constraint.
result Models can reproduce Kolmogorov turbulence characteristics.
We introduce cylindrical projections to simulate infinite-dimensional occupation flows of diffusions.
problem Computational intractability of infinite-dimensional occupation flows of diffusions.
method Introduce cylindrical projections to approximate the occupation flow via a finite-dimensional system.
result Strong convergence of cylindrical projections to the initial process with derived rates.
New method learns discrete graph diffusion via free-energy gradient flows.
problem Challenges in translating continuous diffusion models to discrete spaces.
method Proposes a novel computational approach using a specific metric on the simplex.
result Recover the underlying functional for various graph classes.
Sharp Lipschitz bounds for flow-matching and diffusion models with optimal sampling rates.
problem Establishing optimal Lipschitz regularity for flow-matching and diffusion models.
method Sharp Lipschitz regularity theory for flow-matching vector fields and diffusion-model scores.
result Achieves optimal sampling rate of d / N \sqrt{d}/N d / N for Euler-type samplers in dimension d d d . New theory improves diffusion model convergence for generating data.
problem Improving convergence of diffusion models for data generation.
method Developed a non-asymptotic convergence theory for probability flow ODEs.
result Proves d / ε d/\varepsilon d / ε iterations suffice for approximating target distributions. New method speeds up generative modeling without requiring diffusion steps.
problem Improving the speed and efficiency of generative modeling techniques.
method Probability flow ODE with a corrector step, achieving better dimension dependence.
result Better dimension dependence ( O ( d ) O(\sqrt{d}) O ( d ) vs. O ( d ) O(d) O ( d ) , assuming smoothness of the data distribution).