IDBM - PyTorch

This repository consists of a self-contained implementation (~500 lines of code, neural network model excluded) of the dataset transfer experiment of:

Diffusion Bridge Mixture Transports, Schrödinger Bridge Problems and Generative Modeling.

The following assumptions are made (see the paper, specifically Section 5.4, for more details):

• the reference process is given by $dX_t = σdW_t$ over $t ∈ [0,1]$ for some scalar $σ ≥ 0$ ;
• the initial dataset is MNIST and the terminal dataset is a subset of EMNIST.

Install

Having cloned this repository, the recommended installation procedure is as follows:

1. Create Virtual Environment

Create a new virtual environment and activate it.

For instance, using (Mini)Conda:

conda create -n idbm pip
conda activate idbm

2. Install PyTorch

Install the latest appropriate version of PyTorch according to the official instructions.

3. Install Other Requirements

Install the remaining requirements:

pip install -r requirements.txt

Run

The Python script idbm.py accepts the following options:

python idbm.py [FLAGS]

FLAGS:
    --method=METHOD
        Default: 'IDBM'
    --sigma=SIGMA
        Default: 1.0
    --iterations=ITERATIONS
        Default: 60
    --training_steps=TRAINING_STEPS
        Default: 5000
    --discretization_steps=DISCRETIZATION_STEPS
        Default: 30
    --batch_dim=BATCH_DIM
        Default: 128
    --learning_rate=LEARNING_RATE
        Default: 0.0001
    --grad_max_norm=GRAD_MAX_NORM
        Default: 1.0
    --ema_decay=EMA_DECAY
        Default: 0.999
    --cache_steps=CACHE_STEPS
        Default: 250
    --cache_batch_dim=CACHE_BATCH_DIM
        Default: 2560
    --test_steps=TEST_STEPS
        Default: 5000
    --test_batch_dim=TEST_BATCH_DIM
        Default: 500
    --loss_log_steps=LOSS_LOG_STEPS
        Default: 100
    --imge_log_steps=IMGE_LOG_STEPS
        Default: 1000

The findings of the paper are replicated by the following runs:

# IDBM -- Iterated Diffusion Bridge Mixture Transport:
python idbm.py --method=IDBM --sigma=1.0
python idbm.py --method=IDBM --sigma=0.5
python idbm.py --method=IDBM --sigma=0.2

# BDBM -- Backward Diffusion Bridge Mixture Transport:
python idbm.py --method=IDBM --sigma=1.0 --iterations=1 --training_steps=300000

# DIPF -- Diffusion Iterated Proportional Fitting Transport:
python idbm.py --method=DIPF --sigma=1.0
python idbm.py --method=DIPF --sigma=0.5
python idbm.py --method=DIPF --sigma=0.2

The runs' histories have been persisted on Weights & Biases, to aid reproducibility, analysis and experimentation.