Entering the Era of Discrete Diffusion Models: A Benchmark for Schrödinger Bridges and Entropic Optimal Transport

Xavier Aramayo, Grigoriy Ksenofontov, Aleksei Leonov, Iaroslav Koshelev, Alexander Korotin

This repository contains the official implementation of the paper "Entering the Era of Discrete Diffusion Models: A Benchmark for Schrödinger Bridges and Entropic Optimal Transport", accepted at ICLR 2026.

📌 TL;DR

This paper proposes a benchmark for Schrödinger Bridge (SB) and entropic optimal transport (EOT) methods on discrete spaces, and adapts several continuous SB/EOT approaches to the discrete setting.

📦 CatSBench (Package)

catsbench is the standalone benchmark package. It provides benchmark definitions, evaluation metrics, and reusable utilities, including a Triton-optimized log-sum-exp (LSE) matmul kernel.

📥 Installation

Install the benchmark package via pip:

pip install catsbench

🚀 Quickstart

Load a benchmark definition and its assets from a pretrained repository:

from catsbench import BenchmarkHD

bench = BenchmarkHD.from_pretrained(
    "gregkseno/catsbench",
    "hd_d2_s50_gaussian_a0.02_gaussian",
    init_benchmark=False,  # skip heavy initialization at load time
)

To sample marginals $p_0$ and $p_1$:

x_start, x_end = bench.sample_input_target(32) # ([B=32, D=2], [B=32, D=2])

Or sample them separately:

x_start = bench.sample_input(32) # [B=32, D=2]
x_end = bench.sample_target(32)  # [B=32, D=2]

Important

Both examples above sample independently, i.e., $(x_0, x_1) \sim p_0(x_0),p_1(x_1)$.

To sample from the ground-truth EOT/SB coupling, i.e., $(x_0, x_1) \sim p_0(x_0),q^*(x_1 | x_0)$, use:

x_start = bench.sample_input(32) # [B=32, D=2]
x_end = bench.sample(x_start)    # [B=32, D=2]

Note

See the end-to-end benchmark workflow (initialization, evaluation, metrics, plotting) in notebooks/benchmark_usage.ipynb

---

Reproducing Experiments

This part describes how to run the full training and evaluation pipeline to reproduce paper's results. It explains how to launch experiments for the provided methods (DLightSB, DLightSB-M, CSBM, $\alpha$-CSBM) and evaluate them on the benchmarks.

|-- configs
|   |-- config.yaml   # main Hydra entrypoint
|   |-- callbacks     # Lightning callbacks: benchmark metrics + visualization
|   |-- data          # datamodule/dataset configs
|   |-- experiment    # experiment presets (override bundles)
|   |-- hydra         # Hydra runtime/output settings
|   |-- logger        # logging backends (Comet, W&B, TensorBoard)
|   |-- method        # method-level configs (e.g., CSBM, DLightSB)
|   |-- model         # model architecture configs
|   |-- prior         # reference process configs
|   `-- trainer       # trainer, hardware, precision, runtime configs
|-- logs              # logs, checkpoints, and run artifacts
|-- notebooks         # analysis and baselines
|-- scripts           # bash (+ SLURM) launch scripts
`-- src
    |-- catsbench     # benchmark package code
    |-- data          # Lightning datamodules + reference process implementation
    |-- methods       # training/inference methods (e.g., CSBM, DLightSB)
    |-- metrics       # callbacks computing benchmark metrics
    |-- plotter       # callbacks for plotting samples and trajectories
    |-- utils         # instantiation, logging, common helpers
    `-- run.py        # main entrypoint for training and testing

📦 Dependencies

Create the Anaconda environment using the following command:

conda env update -f environment.yml

and activate it:

conda activate catsbench

🏋️ Training

To start training, pick an experiment config under configs/experiment/<method_name>/benchmark_hd/<exp_name>.yaml and launch it with:

python -m src.run experiment=<method_name>/benchmark_hd/<exp_name>

Example:

python -m src.run experiment=dlight_sb/benchmark_hd/d2_g002

📊 Evaluation

Use the same experiment config as in training and set a checkpoint:

• Manual path: logs/runs/<method_name>/benchmark_hd/<exp_name>/<seed>/<date>/epoch_<...>.ckpt
• Or set ckpt_path=auto to automatically load the latest checkpoint based on the config.

python -m src.run task_name=test ckpt_path=auto \
  experiment=<method_name>/benchmark_hd/<exp_filename>

Example:

python -m src.run task_name=test ckpt_path=auto \
  experiment=dlight_sb/benchmark_hd/d2_g002

🎓 Citation

@misc{
  carrasco2025enteringeradiscretediffusion,
  title={Entering the Era of Discrete Diffusion Models: A Benchmark for {Schr\"odinger} Bridges and Entropic Optimal Transport}, 
  author={Xavier Aramayo Carrasco and Grigoriy Ksenofontov and Aleksei Leonov and Iaroslav Sergeevich Koshelev and Alexander Korotin},
  year={2025},
  eprint={2509.23348},
  archivePrefix={arXiv},
  primaryClass={cs.LG},
  url={https://arxiv.org/abs/2509.23348}, 
}

🙏 Credits

• Comet ML — experiment-tracking and visualization toolkit;
• Inkscape — an excellent open-source editor for vector graphics;
• Hydra/Lightning template - project template used as a starting point.