Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
Go With the Flow: Fast Diffusion for Gaussian Mixture Models
Authors: George Rapakoulias, Ali Reza Pedram, Fengjiao Liu, Lingjiong Zhu, Panagiotis Tsiotras
NeurIPS 2025 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | 5 Experiments 2D Problems and Benchmarks. We first test the algorithm in various 2D toy problems as shown, for example, in Figure 1 for a Gaussian-to-Gaussian Mixture problem for various noise levels. To assess optimality, we evaluate the resulting transport cost for policy (13) for each noise level and compare it with the upper bound from (15a). We also run a series of EOT benchmarks and compare them with state-of-the-art neural approaches such as the DSB (De Bortoli et al., 2021) and DSBM (Shi ets al., 2023) algorithms. ... Image-to-Image Translation. Following Korotin et al. (2024), we use our algorithm in the latent space of an autoencoder to perform a man-to-woman and adult-to-child image translation task. ... To test how well the generated images match the features of the given target distribution, we calculate the Fr echet inception distance (FID) scores (Heusel et al., 2017) between the actual and the generated images of a given class, using 10,000 samples from each distribution. ... Multi-Marginal Problems. A key challenge in SBs is learning a system s underlying diffusion process, given samples from partial observations of the distribution of its state, measured at regular time intervals (Chen et al., 2023). ... We visualize the data generated by our method in Figure 4, and provide standard performance metrics in Table 3. Specifically, following Chen et al. (2023), we use the Sliced Wasserstein Distance (SWD) and Maximum Mean Discrepancy (MMD) metrics averaged over the 4 predicted time marginals of the dataset. |
| Researcher Affiliation | Academia | George Rapakoulias 1 Ali Reza Pedram 1,2 Fengjiao Liu 3 Lingjiong Zhu 4 Panagiotis Tsiotras 1 1 Department of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 2 School of Computer Science, University of Oklahoma, Norman, OK 3 Department of ECE, FAMU-FSU College of Engineering, Tallahassee, FL 4 Department of Mathematics, Florida State University, Tallahassee, FL Corresponding author: EMAIL |
| Pseudocode | Yes | Algorithm 1 GMMflow training ... Algorithm 2 GMMflow inference ... Algorithm 3 Multi-marginal GMMflow inference |
| Open Source Code | Yes | The implementation is publicly available at https://github.com/george Rapa/GMMflow. |
| Open Datasets | Yes | We use the pre-trained ALAE autoencoder (Pidhorskyi et al., 2020), trained on the FFHQ dataset (Karras et al., 2021). ... To showcase the effectiveness of our approach in such problems, we consider the sc RNA-seq dataset from (Moon et al., 2019), with the pre-processing detailed in Tong et al. (2020). ... To compare our approach for the problem of Figure 1 with state-of-the-art neural SB solvers we used the original implementations of the DSB4 (De Bortoli et al., 2021) and DSBM5 (Shi et al., 2023). ... To further evaluate the optimality of the proposed approach, we tested the algorithm on the Entropic Optimal Transport benchmark detailed in Gushchin et al. (2023). |
| Dataset Splits | No | The paper mentions fitting GMMs to samples of boundary distributions and using 10,000 samples for FID score calculation, but it does not specify explicit training, validation, or test splits for the GMM fitting or policy calculation steps. For the scRNA-seq dataset, it mentions data grouped at 5 regular time intervals and taking the first 5 PCs, but again, no train/test/validation splits are detailed for model training. |
| Hardware Specification | Yes | All tests were conducted on a desktop computer with an RTX 3070 GPU. ... This brought down the total calculation time under 6 minutes. For the final policy calculation, there are only 21 active GMSBs in the mixture policy (18), each taking 6 seconds to compute. The total run time for our algorithm for this problem, adds up to 8 minutes for this problem, which is considerably lower than the corresponding neural methods (24 minutes on GPU for the DMSB algorithm (Chen et al., 2023)). ... The computation of each one using the coarse time grid takes roughly 0.35 s on an Intel i7 12-th generation CPU with 32 GB of RAM memory, giving a total of 18.5 minutes of calculations, if all GMSBs are solved serially. |
| Software Dependencies | No | The paper mentions using MOSEK (Mosek, 2020) for solving LP problems, the POT library (Flamary et al., 2021) for discrete optimal transport, and scipy (Virtanen et al., 2020) for inverse CDFs. While these tools are cited with their publication years, specific version numbers (e.g., MOSEK 10.0, scipy 1.7.0) are not explicitly provided as required by the guidelines. |
| Experiment Setup | Yes | We start by fitting a 10-component mixture model to the embeddings of each image class, with diagonal covariance matrices to facilitate matrix inversions in the Gaussian-to-Gaussian policy calculations summarized in Proposition 1, and then apply Algorithms 1, 2 for ϵ = 0.01. ... For our setup, we keep the first 5 PCs from the 5 marginal distributions, and prefit 5-component GMMs in each marginal. We use the second-order model (16b) to capture the prior dynamics and the structure of the system; however, we note that any LTV model with structure of the form (11) would be applicable. ... Specifically, we assume the GMMs between the five temporal marginals are spaced 1 time unit apart, resulting in a problem horizon of 4 time units. We use a coarse temporal discretization with time-step t = 0.1 (i.e., 10 time steps between [ti, ti+1]) to evaluate the cost tensor for the optimization problem (20) and a fine resolution discretization of t = 0.01 for the final policy calculation, solving only for the GMSBs with non-zero transport parameter λi. |