Simulation-free Schr\"odinger bridges via score and flow matching
- URL: http://arxiv.org/abs/2307.03672v3
- Date: Mon, 11 Mar 2024 14:42:58 GMT
- Title: Simulation-free Schr\"odinger bridges via score and flow matching
- Authors: Alexander Tong, Nikolay Malkin, Kilian Fatras, Lazar Atanackovic,
Yanlei Zhang, Guillaume Huguet, Guy Wolf, Yoshua Bengio
- Abstract summary: We present simulation-free score and flow matching ([SF]$2$M)
Our method generalizes both the score-matching loss used in the training of diffusion models and the recently proposed flow matching loss used in the training of continuous flows.
Notably, [SF]$2$M is the first method to accurately model cell dynamics in high dimensions and can recover known gene regulatory networks simulated data.
- Score: 89.4231207928885
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We present simulation-free score and flow matching ([SF]$^2$M), a
simulation-free objective for inferring stochastic dynamics given unpaired
samples drawn from arbitrary source and target distributions. Our method
generalizes both the score-matching loss used in the training of diffusion
models and the recently proposed flow matching loss used in the training of
continuous normalizing flows. [SF]$^2$M interprets continuous-time stochastic
generative modeling as a Schr\"odinger bridge problem. It relies on static
entropy-regularized optimal transport, or a minibatch approximation, to
efficiently learn the SB without simulating the learned stochastic process. We
find that [SF]$^2$M is more efficient and gives more accurate solutions to the
SB problem than simulation-based methods from prior work. Finally, we apply
[SF]$^2$M to the problem of learning cell dynamics from snapshot data. Notably,
[SF]$^2$M is the first method to accurately model cell dynamics in high
dimensions and can recover known gene regulatory networks from simulated data.
Our code is available in the TorchCFM package at
https://github.com/atong01/conditional-flow-matching.
Related papers
- Reducing Spatial Discretization Error on Coarse CFD Simulations Using an OpenFOAM-Embedded Deep Learning Framework [0.7223509567556214]
We propose a method for enhancing the quality of low-resolution simulations using a deep learning model fed with high-quality data.
We substitute the default differencing scheme for the convection term by a feed-forward neural network that interpolates velocities from cell centers to face values.
The deep learning framework incorporates the open-source CFD code OpenFOAM, resulting in an end-to-end differentiable model.
arXiv Detail & Related papers (2024-05-13T02:59:50Z) - Improving and generalizing flow-based generative models with minibatch
optimal transport [90.01613198337833]
We introduce the generalized conditional flow matching (CFM) technique for continuous normalizing flows (CNFs)
CFM features a stable regression objective like that used to train the flow in diffusion models but enjoys the efficient inference of deterministic flow models.
A variant of our objective is optimal transport CFM (OT-CFM), which creates simpler flows that are more stable to train and lead to faster inference.
arXiv Detail & Related papers (2023-02-01T14:47:17Z) - Flow Annealed Importance Sampling Bootstrap [11.458583322083125]
Flow AIS Bootstrap (FAB) is a tractable density model that approximates complex target distributions.
We show that FAB produces better results than training via maximum likelihood on MD samples while using 100 times fewer target evaluations.
We are the first to learn the Boltzmann distribution of the alanine dipeptide molecule using only the target density.
arXiv Detail & Related papers (2022-08-03T07:44:48Z) - Manifold Interpolating Optimal-Transport Flows for Trajectory Inference [64.94020639760026]
We present a method called Manifold Interpolating Optimal-Transport Flow (MIOFlow)
MIOFlow learns, continuous population dynamics from static snapshot samples taken at sporadic timepoints.
We evaluate our method on simulated data with bifurcations and merges, as well as scRNA-seq data from embryoid body differentiation, and acute myeloid leukemia treatment.
arXiv Detail & Related papers (2022-06-29T22:19:03Z) - FKreg: A MATLAB toolbox for fast Multivariate Kernel Regression [5.090316990822874]
We introduce a new toolbox for fast multivariate kernel regression with the idea of non-uniform FFT (NUFFT)
NUFFT implements the algorithm for $M$ gridding points with $Oleft( N+Mlog M right)$ complexity and accuracy controllability.
The bandwidth selection problem utilizes the Fast Monte-Carlo to estimate the degree of freedom.
arXiv Detail & Related papers (2022-04-16T04:52:44Z) - Learning Free-Surface Flow with Physics-Informed Neural Networks [0.0]
We build on the notion of physics-informed neural networks (PINNs) and employ them in the area of shallow-water equation (SWE) models.
These models play an important role in modeling and simulating free-surface flow scenarios such as in flood-wave propagation or tsunami waves.
arXiv Detail & Related papers (2021-11-17T18:45:55Z) - Inverting brain grey matter models with likelihood-free inference: a
tool for trustable cytoarchitecture measurements [62.997667081978825]
characterisation of the brain grey matter cytoarchitecture with quantitative sensitivity to soma density and volume remains an unsolved challenge in dMRI.
We propose a new forward model, specifically a new system of equations, requiring a few relatively sparse b-shells.
We then apply modern tools from Bayesian analysis known as likelihood-free inference (LFI) to invert our proposed model.
arXiv Detail & Related papers (2021-11-15T09:08:27Z) - Discrete Denoising Flows [87.44537620217673]
We introduce a new discrete flow-based model for categorical random variables: Discrete Denoising Flows (DDFs)
In contrast with other discrete flow-based models, our model can be locally trained without introducing gradient bias.
We show that DDFs outperform Discrete Flows on modeling a toy example, binary MNIST and Cityscapes segmentation maps, measured in log-likelihood.
arXiv Detail & Related papers (2021-07-24T14:47:22Z) - Borrowing From the Future: Addressing Double Sampling in Model-free
Control [8.282602586225833]
This paper extends the BFF algorithm to action-value function based model-free control.
We prove that BFF is close to unbiased SGD when the underlying dynamics vary slowly with respect to actions.
arXiv Detail & Related papers (2020-06-11T03:50:37Z) - Quantum Algorithms for Simulating the Lattice Schwinger Model [63.18141027763459]
We give scalable, explicit digital quantum algorithms to simulate the lattice Schwinger model in both NISQ and fault-tolerant settings.
In lattice units, we find a Schwinger model on $N/2$ physical sites with coupling constant $x-1/2$ and electric field cutoff $x-1/2Lambda$.
We estimate observables which we cost in both the NISQ and fault-tolerant settings by assuming a simple target observable---the mean pair density.
arXiv Detail & Related papers (2020-02-25T19:18:36Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.