Papers › FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models

FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models

2 Oct 2018ICLR 2019 5arXiv:1810.01367archive 2025-07-28

Will Grathwohl, Ricky T. Q. Chen, Jesse Bettencourt, Ilya Sutskever, David Duvenaud

A promising class of generative models maps points from a simple distribution to a complex distribution through an invertible neural network. Likelihood-based training of these models requires restricting their architectures to allow cheap computation of Jacobian determinants. Alternatively, the Jacobian trace can be used if the transformation is specified by an ordinary differential equation. In this paper, we use Hutchinson's trace estimator to give a scalable unbiased estimate of the log-density. The result is a continuous-time invertible generative model with unbiased density estimation and one-pass sampling, while allowing unrestricted neural network architectures. We demonstrate our approach on high-dimensional density estimation, image generation, and variational inference, achieving the state-of-the-art among exact likelihood methods with efficient sampling.

PaperPDFConference PDFCodeCode Syntology ran

In Syntology Open this paper in Syntology's Atlas, the map of the papers in Syntology's graph and their citations.

For agents, Syntology's MCP tool lists every function and class Syntology harvested from this paper and whether it ran (how to connect): get_harvested_code_for_paper(arxiv_id="1810.01367")

Code

Syntology Ran 4 of 5 code samples harvested from 3 repositories linked to this paper; 1 has no recorded run. Of those that ran: 4 ran with no contract checked.

By repository: community (archive-listed): 5 samples from 3 repositories, 4 ran. The run record, sample by sample. “Ran” means executed on a synthesized input, not that the code is correct or reproduces the paper.

BorealisAI/continuous-time-flow-process mentioned on GitHubpytorch report
jackgoffinet/ffjord-lite mentioned on GitHubpytorch report
jacobjinkelly/easy-neural-ode mentioned on GitHubjax report
lenz3000/ffjord-path mentioned on GitHubpytorch report
mandubian/pytorch-neural-ode mentioned on GitHubpytorchNOASSERTION report
rtqichen/ffjord mentioned on GitHubpytorch report

Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.

Code Syntology ran Syntology

5 samples harvested; 4 ran; 0 honoured the contract we drafted; 1 has no recorded run. Read from Syntology's graph 2026-09-24; that is when this build read the record, not when the samples ran.

4ran
1unverified

Licence: 0 of the 5 samples are pointer only, meaning Syntology does not serve that copy's text. This page shows no code text for any sample; each one links to its file in the repository.

Harvested from 3 repositories linked to this paper, official or community; each sample names its own and says which. “Ran” means the sample executed on a synthesized input. It does not mean the output is correct, and nothing here reproduces the paper's results. “Honoured” and “violated” refer to a contract Syntology drafted from the code itself; “our draft was wrong” and “fixture could not drive it” are failures of Syntology's instrument, not of the code.

Each sample ends with its code_sha256, Syntology's identity for that exact code. An agent fetches the stored sample with Syntology's MCP tool get_code(code_sha256="…") (how to connect); click an identity to copy that call.

Repository labels, per sample. official repository: The archive marks this repository official for the paper. named in the paper: The archive records that the paper mentions this repository; it is not marked official. community (archive-listed): In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper. found in paper text by Syntology: Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted. community: Not in the archive's code links for this paper; a community repository Syntology harvested. Samples from a repository marked official are listed first. Licence labels name the repository's licence as recorded at harvest. “Pointer only” means Syntology does not serve that copy's text, for one of four reasons: no licence file was found; the licence was not identified; the licence is recorded as permissive but that copy's record is not marked cleared; or the licence is outside the permissive list Syntology serves text under (MIT, Apache-2.0, BSD and similar). Some licences outside that list permit redistribution, such as WTFPL, and GPL-3.0 under its conditions; they are simply not on the list. Hover a licence label for the reason. File links open the file on GitHub at the default branch, which may have changed since the harvest.

CNF rtqichen/ffjord/lib/layers/cnf.py community (archive-listed) ran fingerprinted MIT (permissive) · 95a9c83deee45d05 · report
FfjordModel jackgoffinet/ffjord-lite/script.py community (archive-listed) ran MIT (permissive) · cc866c798f64c000 · report
ODEfunc jackgoffinet/ffjord-lite/script.py community (archive-listed) ran · metamorphic tier: deterministic MIT (permissive) · bc4c9f15c07b078a · report
RegularizedODEfunc rtqichen/ffjord/lib/layers/cnf.py community (archive-listed) ran fingerprinted MIT (permissive) · 846f94d3f2e1378b · report
ODEfunc lenz3000/ffjord-path/lib/layers/odefunc.py community (archive-listed) unverified MIT (permissive) · def28b9e7df60464 · report

Tasks

Density EstimationFormImage GenerationVariational Inference

Results from the paper archive 2025-07-28

TaskDatasetModelMetricValueRank at snapshotLeaderboardReport
Density Estimation BSDS300 FFJORD CD 0.683 #2 of 5 Archive leaderboard report
Density Estimation BSDS300 FFJORD EMD 0.0281 #2 of 5 Archive leaderboard report
Density Estimation BSDS300 FFJORD Log-likelihood 157.4 #2 of 5 Archive leaderboard report
Density Estimation BSDS300 FFJORD MMD-CD 0.548 #2 of 5 Archive leaderboard report
Density Estimation BSDS300 FFJORD MMD-EMD 0.0227 #2 of 5 Archive leaderboard report
Density Estimation BSDS300 FFJORD NLL -157.4 #2 of 5 Archive leaderboard report
Density Estimation CIFAR-10 FFJORD NLL (bits/dim) 3.4 #12 of 15 Archive leaderboard report
Density Estimation Caltech-101 FFJORD COV-L2 98.8% #2 of 3 Archive leaderboard report
Density Estimation Caltech-101 FFJORD MMD-L2 18.6 #2 of 3 Archive leaderboard report
Density Estimation Caltech-101 FFJORD Negative ELBO 104.03 #2 of 3 Archive leaderboard report
Density Estimation Freyfaces FFJORD COV-L2 100% #2 of 3 Archive leaderboard report
Density Estimation Freyfaces FFJORD MMD-L2 0.834 #2 of 3 Archive leaderboard report
Density Estimation Freyfaces FFJORD Negative ELBO 4.39 #2 of 3 Archive leaderboard report
Density Estimation MNIST FFJORD COV-L2 96.4% #3 of 6 Archive leaderboard report
Density Estimation MNIST FFJORD MMD-L2 17.3 #3 of 6 Archive leaderboard report
Density Estimation MNIST FFJORD NLL (bits/dim) 0.99 #3 of 6 Archive leaderboard report
Density Estimation OMNIGLOT FFJORD COV-L2 99% #2 of 4 Archive leaderboard report
Density Estimation OMNIGLOT FFJORD MMD-L2 20.5 #2 of 4 Archive leaderboard report
Density Estimation OMNIGLOT FFJORD Negative ELBO 98.33 #2 of 4 Archive leaderboard report
Density Estimation UCI GAS FFJORD CD 1.29 #3 of 5 Archive leaderboard report
Density Estimation UCI GAS FFJORD EMD 0.146 #3 of 5 Archive leaderboard report
Density Estimation UCI GAS FFJORD Log-likelihood 8.59 #3 of 5 Archive leaderboard report
Density Estimation UCI GAS FFJORD MMD-CD 0.95 #3 of 5 Archive leaderboard report
Density Estimation UCI GAS FFJORD MMD-EMD 0.135 #3 of 5 Archive leaderboard report
Density Estimation UCI HEPMASS FFJORD CD 13.8 #1 of 5 Archive leaderboard report
Density Estimation UCI HEPMASS FFJORD EMD 0.164 #1 of 5 Archive leaderboard report
Density Estimation UCI HEPMASS FFJORD Log-likelihood -14.92 #1 of 5 Archive leaderboard report
Density Estimation UCI HEPMASS FFJORD MMD-CD 13.8 #1 of 5 Archive leaderboard report
Density Estimation UCI HEPMASS FFJORD MMD-EMD 0.158 #1 of 5 Archive leaderboard report
Density Estimation UCI HEPMASS FFJORD NLL 14.92 #1 of 5 Archive leaderboard report
Density Estimation UCI MINIBOONE FFJORD CD 24.6 #2 of 5 Archive leaderboard report
Density Estimation UCI MINIBOONE FFJORD EMD 0.27 #2 of 5 Archive leaderboard report
Density Estimation UCI MINIBOONE FFJORD Log-likelihood -10.43 #2 of 5 Archive leaderboard report
Density Estimation UCI MINIBOONE FFJORD MMD-CD 24.1 #2 of 5 Archive leaderboard report
Density Estimation UCI MINIBOONE FFJORD MMD-EMD 0.254 #2 of 5 Archive leaderboard report
Density Estimation UCI MINIBOONE FFJORD NLL 10.43 #2 of 5 Archive leaderboard report
Density Estimation UCI POWER FFJORD CD 0.153 #4 of 6 Archive leaderboard report
Density Estimation UCI POWER FFJORD EMD 0.116 #4 of 6 Archive leaderboard report
Density Estimation UCI POWER FFJORD Log-likelihood 0.46 #4 of 6 Archive leaderboard report
Density Estimation UCI POWER FFJORD MMD-CD 0.144 #4 of 6 Archive leaderboard report
Density Estimation UCI POWER FFJORD MMD-EMD 0.111 #4 of 6 Archive leaderboard report
Density Estimation UCI POWER FFJORD NLL -0.46 #4 of 6 Archive leaderboard report

Ranks are positions in the archive's leaderboards as they stood at the 2025-07-28 snapshot. Results published since then are not among these rows, so a rank here is not a current standing.

Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections