MCMC + Diffusion Sampling

Sam Foreman

MCMC + Diffusion Sampling

April 15, 2024

Denoising Diffusion Probabilistic Models

Imports / Setup

from __future__ import absolute_import, print_function, annotations, division
from dataclasses import dataclass

import sys
import os
import math
import numpy as np
import scipy
import time
from random import randrange
import matplotlib.pyplot as plt
import seaborn as sns
import numpy as np

from ezpz.dist import setup_torch

port = np.random.randint(5000, 6000)
print(f"Using port: {port}")

RANK = setup_torch(
    backend="DDP",
    port=f"{port}"
)

Using port: 5561

Using DDP for distributed training

Global Rank: 0 / 0

:::

%matplotlib inline
import matplotlib_inline
matplotlib_inline.backend_inline.set_matplotlib_formats('svg')

from l2hmc.main import build_experiment
from l2hmc.utils.rich import get_console
from l2hmc.utils.plot_helpers import set_plot_style

import opinionated
from l2hmc.diffusion.diffusion import PureMH, MH_Diffusion
from l2hmc.utils.plot_helpers import set_plot_style

from pandas.io.formats import style
import scipy
import time
from random import randrange
from l2hmc.diffusion.diffusion import PureMH, MH_Diffusion

set_plot_style()
console = get_console()
print(console.is_jupyter)
if console.is_jupyter:
    console.is_jupyter = False
print(console.is_jupyter)

Using device: cpu

Failed to download font: Source Sans Pro, skipping! Failed to download font: Titillium WebRoboto Condensed, skipping!

True

False

plt.style.use(opinionated.STYLES['opinionated_min'])
sns.set_context('notebook')

2D U(1)

from l2hmc.configs import dict_to_list_of_overrides

seed = np.random.randint(0, 2**32)
console.print(f"seed = {seed}")

overrides = {
    "seed": f"{seed}",
    "precision": "float32",
    "init_wandb": False,
    "init_aim": False,
    "use_wandb": False,
    "dynamics": {
        "latvolume": [32, 32],
        "nleapfrog": 10,
        "nchains": 16,
        "eps": 0.05,
    },
    "network": {
        "use_batch_norm": False,
    },
    'annealing_schedule': {
        'beta_init': 6.0,
        'beta_final': 6.0,
    },

}
OVERRIDES = dict_to_list_of_overrides(overrides)

seed = 1675333995

from pathlib import Path
from l2hmc.common import get_timestamp
from enrich.console import get_theme, Console
console = Console(theme=get_theme())

OUTDIR = Path(
    'l2hmc-diffusion-2dU1'
).joinpath(get_timestamp("%Y-%m-%d"))
OUTDIR.mkdir(exist_ok=True, parents=True)
console.print(f"OUTDIR: {OUTDIR}")

date = get_timestamp('%Y-%m-%d')
PLOTS_DIR = OUTDIR.joinpath('plots')
PLOTS_DIR.mkdir(exist_ok=True, parents=True)
console.print(f"Saving figures to: {PLOTS_DIR}")

OUTDIR: l2hmc-diffusion-2dU1/2023-09-21

Saving figures to: l2hmc-diffusion-2dU1/2023-09-21/plots

#os.environ['MASTER_PORT'] = '5436'

exp = build_experiment(
    overrides=[
        *OVERRIDES,
        'framework=pytorch',
        'backend=DDP'
    ]
)

[09/21/23 12:23:55][INFO][dist.py:226] - Caught MASTER_PORT:5561 from environment!
[09/21/23 12:23:55][INFO][dist.py:338] - Global Rank: 0 / 0
[09/21/23 12:23:58][INFO][experiment.py:251] - Creating outputs/2023-09-21-122358/pytorch/train
[09/21/23 12:23:58][INFO][experiment.py:251] - Creating outputs/2023-09-21-122358/pytorch/eval
[09/21/23 12:23:58][INFO][experiment.py:251] - Creating outputs/2023-09-21-122358/pytorch/hmc
[09/21/23 12:23:58][INFO][dist.py:226] - Caught MASTER_PORT:5561 from environment!
[09/21/23 12:23:58][INFO][dist.py:226] - Caught MASTER_PORT:5561 from environment!
[09/21/23 12:24:06][INFO][trainer.py:441] - Looking for checkpoints in:
 /Users/samforeman/projects/saforem2/l2hmc-qcd/src/l2hmc/checkpoints/U1/2-32-32/nlf-10/xsplit-True/sepnets-True/merge-True/conv-8-16-32-64-128_5-3-3-3-2_2-2-2-2-2/net-16-16-16-16_dp-0.2_bn-False/pytorch
[09/21/23 12:24:06][WARNING][trainer.py:437] - No checkpoints found to load from
[09/21/23 12:24:06][WARNING][trainer.py:437] - Restoring global step from ckpt! self._gstep: 0
[09/21/23 12:24:06][WARNING][trainer.py:437] - Using `torch.optim.Adam` optimizer
[09/21/23 12:24:06][INFO][trainer.py:284] - num_params in model: 958628260
[09/21/23 12:24:09][WARNING][trainer.py:250] - logging with freq 50 for wandb.watch

state = exp.trainer.dynamics.random_state(6.0)
xdim = state.x.flatten().shape[0]

dim = xdim
low_bound = (-np.pi) * np.ones(dim)
high_bound = (np.pi) * np.ones(dim)
sigma = 0.15
retrains = 10
samples_per_retrain = 100
diffusion_prob = 0.1

sns.set_context('notebook')

outputs = {}
outputs['hmc'] = exp.trainer.eval(
    job_type='hmc',
    beta=6.0,
    nprint=100,
    nchains=16,
    eval_steps=1000
)
#hdset = exp.save_dataset(job_type='hmc', nchains=1)

[09/21/23 12:24:21][WARNING][trainer.py:437] - Step size `eps` not specified for HMC! Using default: 0.1000 for generic HMC
[09/21/23 12:24:21][WARNING][trainer.py:437] - x.shape (original): torch.Size([16, 2, 32, 32])
[09/21/23 12:24:21][WARNING][trainer.py:437] - x[:nchains].shape: torch.Size([16, 2, 32, 32])
[09/21/23 12:24:21][INFO][trainer.py:1058] - eps=0.1
beta=6.0
nlog=10
table=<rich.table.Table object at 0x2e1b98520>
nprint=100
eval_steps=1000
nleapfrog=20

[09/21/23 12:24:24][INFO][trainer.py:1188] - hstep=0 dt=0.024 beta=6.000 loss=3.410 dQsin=0.125 dQint=0.000 energy=1586.502 logprob=1586.502 logdet=0.000 acc=0.472 sumlogdet=0.000 acc_mask=0.500 plaqs=0.909 intQ=0.000 sinQ=0.051
[09/21/23 12:24:27][INFO][trainer.py:1188] - hstep=100 dt=0.026 beta=6.000 loss=2.876 dQsin=0.163 dQint=0.000 energy=1555.800 logprob=1555.800 logdet=0.000 acc=0.593 sumlogdet=0.000 acc_mask=0.688 plaqs=0.912 intQ=-0.125 sinQ=-0.159
[09/21/23 12:24:31][INFO][trainer.py:1188] - hstep=200 dt=0.025 beta=6.000 loss=4.678 dQsin=0.088 dQint=0.063 energy=1569.994 logprob=1569.994 logdet=0.000 acc=0.451 sumlogdet=0.000 acc_mask=0.250 plaqs=0.912 intQ=-0.187 sinQ=-0.149
[09/21/23 12:24:34][INFO][trainer.py:1188] - hstep=300 dt=0.024 beta=6.000 loss=14.041 dQsin=0.094 dQint=0.000 energy=1554.118 logprob=1554.118 logdet=0.000 acc=0.438 sumlogdet=0.000 acc_mask=0.438 plaqs=0.914 intQ=-0.125 sinQ=-0.114
[09/21/23 12:24:38][INFO][trainer.py:1188] - hstep=400 dt=0.024 beta=6.000 loss=-0.739 dQsin=0.199 dQint=0.000 energy=1566.516 logprob=1566.516 logdet=0.000 acc=0.509 sumlogdet=0.000 acc_mask=0.562 plaqs=0.912 intQ=-0.437 sinQ=-0.452
[09/21/23 12:24:41][INFO][trainer.py:1188] - hstep=500 dt=0.045 beta=6.000 loss=1.545 dQsin=0.100 dQint=0.000 energy=1570.837 logprob=1570.837 logdet=0.000 acc=0.448 sumlogdet=0.000 acc_mask=0.562 plaqs=0.911 intQ=0.125 sinQ=0.189
[09/21/23 12:24:45][INFO][trainer.py:1188] - hstep=600 dt=0.025 beta=6.000 loss=3.780 dQsin=0.094 dQint=0.000 energy=1568.012 logprob=1568.012 logdet=0.000 acc=0.463 sumlogdet=0.000 acc_mask=0.500 plaqs=0.913 intQ=0.438 sinQ=0.466
[09/21/23 12:24:50][INFO][trainer.py:1188] - hstep=700 dt=0.023 beta=6.000 loss=-0.902 dQsin=0.113 dQint=0.000 energy=1563.778 logprob=1563.778 logdet=0.000 acc=0.475 sumlogdet=0.000 acc_mask=0.375 plaqs=0.913 intQ=0.688 sinQ=0.628
[09/21/23 12:24:53][INFO][trainer.py:1188] - hstep=800 dt=0.024 beta=6.000 loss=11.416 dQsin=0.061 dQint=0.000 energy=1561.427 logprob=1561.427 logdet=0.000 acc=0.339 sumlogdet=0.000 acc_mask=0.438 plaqs=0.913 intQ=0.813 sinQ=0.755
[09/21/23 12:24:57][INFO][trainer.py:1188] - hstep=900 dt=0.028 beta=6.000 loss=1.114 dQsin=0.127 dQint=0.000 energy=1564.465 logprob=1564.465 logdet=0.000 acc=0.699 sumlogdet=0.000 acc_mask=0.625 plaqs=0.913 intQ=0.938 sinQ=0.893

# %matplotlib inline
from l2hmc.common import plot_dataset
sns.set_context('notebook')
hdataset = outputs['hmc']['history'].get_dataset()
plot_dataset(hdataset, outdir=PLOTS_DIR, job_type='HMC')

[09/21/23 12:25:06][INFO][plot_helpers.py:1049] - Saving figure to: l2hmc-diffusion-2dU1/2023-09-21/plots/ridgeplots/svgs/energy_ridgeplot.svg
[09/21/23 12:25:09][INFO][plot_helpers.py:1049] - Saving figure to: l2hmc-diffusion-2dU1/2023-09-21/plots/ridgeplots/svgs/logprob_ridgeplot.svg
[09/21/23 12:25:11][INFO][plot_helpers.py:1049] - Saving figure to: l2hmc-diffusion-2dU1/2023-09-21/plots/ridgeplots/svgs/logdet_ridgeplot.svg

import torch

initial_states = []
state_init = exp.trainer.dynamics.random_state(6.0)
x = state_init.x
beta = state_init.beta

NSAMPLES = 1000
for idx in range(NSAMPLES + int(0.1 * NSAMPLES)):
    if idx % 100 == 0:
        console.print(f"step: {idx}")
        
    x, metrics = exp.trainer.hmc_step((x, beta))
    if idx > int((0.1 * NSAMPLES)):
        initial_states.append(x)

initial_states = torch.stack(initial_states).squeeze()
initial_states_np = initial_states.detach().cpu().numpy()

step: 0

step: 100

step: 200

step: 300

step: 400

step: 500

step: 600

step: 700

step: 800

step: 900

step: 1000

initial_states_np.shape

(999, 16, 2048)

x_ = initial_states_np.reshape(-1, 16, 2, 32, 32)
tmp_ = x_[:, 0, ...]
console.print(f'{x_.shape}')
console.print(f'{tmp_.shape}')

(999, 16, 2, 32, 32)

(999, 2, 32, 32)

from l2hmc.common import savefig

#x_ = initial_states_np[:100].reshape(-1, 2, 32, 32)
tmp_ = x_[:, 0, ...]
fig, ax = plt.subplots()
sns.kdeplot(
    x=tmp_[-100:, 0].flatten(),
    y=tmp_[-100:, 1].flatten(),
    # ax=ax,
    cmap='viridis',
    # ax=axes[0],
    # cmap="Blues",
    shade=False,
    # bw_adjust=0.5,
    thresh=0
)
ax.set_xlim((-4, 4))
ax.set_ylim((-4, 4))
savefig(
    f'hmc_samples-{NSAMPLES}',
    Path(PLOTS_DIR),
    tstamp=True,
)

Saving hmc_samples-1000-2023-09-21-122840 to l2hmc-diffusion-2dU1/2023-09-21/plots

class Diffusion:
    def __init__(
            self,
            noise_steps: int = 1000,
            beta_start: float = 1e-4,
            beta_end: float = 0.02,
            nchannels: int = 2,
            img_size: int = 256,
            device: str = "cuda"
    ):
        self.noise_steps = noise_steps
        self.beta_start = beta_start
        self.beta_end = beta_end
        self.img_size = img_size
        self.device = device
        self.nchannels = nchannels

        self.beta = self.prepare_noise_schedule().to(device)
        self.alpha = 1. - self.beta
        self.alpha_hat = torch.cumprod(self.alpha, dim=0)

    def prepare_noise_schedule(self):
        return torch.linspace(self.beta_start, self.beta_end, self.noise_steps)

    def noise_images(self, x, t):
        sqrt_alpha_hat = torch.sqrt(self.alpha_hat[t])[:, None, None, None]
        sqrt_one_minus_alpha_hat = torch.sqrt(
            1 - self.alpha_hat[t]
        )[:, None, None, None]
        eps = torch.randn_like(x)
        return sqrt_alpha_hat * x + sqrt_one_minus_alpha_hat * eps, eps

    def sample_timesteps(self, n):
        return torch.randint(low=1, high=self.noise_steps, size=(n,))

    def sample(self, model, n):
        # console.print(f"Sampling {n} new images....")
        model.eval()
        with torch.no_grad():
            x = torch.randn(
                (n, self.nchannels, self.img_size, self.img_size)
            ).to(self.device)
            sample_bar = tqdm(
                reversed(range(1, self.noise_steps)),
                position=0,
                total=self.noise_steps - 1,
                dynamic_ncols=True,
            )
            for i in sample_bar:
                t = (torch.ones(n) * i).long().to(self.device)
                predicted_noise = model(x, t)
                alpha = self.alpha[t][:, None, None, None]
                alpha_hat = self.alpha_hat[t][:, None, None, None]
                beta = self.beta[t][:, None, None, None]
                if i > 1:
                    noise = torch.randn_like(x)
                else:
                    noise = torch.zeros_like(x)
                x = (
                    (1 / torch.sqrt(alpha))
                    * (
                        x 
                        - ((1 - alpha) / (torch.sqrt(1 - alpha_hat)))
                        * predicted_noise
                    ) 
                    + (torch.sqrt(beta) * noise)
                )
        model.train()
        x = (x + np.pi) % (2 * np.pi) - np.pi
        return x

initial_states.shape

torch.Size([999, 16, 2048])

Train Diffusion Model

import torchvision
import os
import random
from pathlib import Path
import torch
import torchvision
import torchvision.transforms as T
import numpy as np
from PIL import Image
#from fastdownload import FastDownload
from torch.utils.data import DataLoader

def save_images(images, path, **kwargs):
    grid = torchvision.utils.make_grid(images, **kwargs)
    ndarr = grid.permute(1, 2, 0).to('cpu').numpy()
    im = Image.fromarray(ndarr)
    im.save(path)

Build Diffusion Model with UNet Architecure

from torch import nn
from torch import optim
import torch.nn.functional as F
from tqdm.auto import tqdm
from torch.utils.data import DataLoader
from torch.utils.data import TensorDataset

from l2hmc.common import savefig
from l2hmc.diffusion.modules import NoiseScheduler, UNet
from l2hmc.diffusion import ddpm

DEVICE = 'cuda' if torch.cuda.is_available() else 'cpu'

config = {
    'channels_in': 2,
    'channels_out': 2,
    'train_batch_size': 5,
    'learning_rate': 0.001,
    'num_epochs': 1,
    'noise_steps': 100,
    'beta': 6.0,
    'img_size': 32,
    'retrains': 10,
    'samples_per_retrain': 500,
    'diffusion_prob': 0.1,
}

model = UNet(c_in=2, c_out=2)

dataset = TensorDataset(initial_states.reshape(-1, 2, 32, 32))
dataloader = DataLoader(
    dataset,
    batch_size=config["train_batch_size"],
    shuffle=False,
    drop_last=True
)


optimizer = optim.AdamW(model.parameters(), lr=config['learning_rate'])
mse = nn.MSELoss()
diffusion = Diffusion(
    noise_steps=100,
    img_size=32,
    device=DEVICE,
    nchannels=2,
)
#logger = SummaryWriter(os.path.join("runs", args.run_name))
l = len(dataloader)

run_name = 'diffusion2dU1'

Perform initial training on HMC samples

from torch import optim
device = 'cpu'
#dataloader = get_data(args)
#model = UNet().to(device)

sampled_images_history = []

for epoch in range(config['num_epochs']):
    console.print(f"Starting epoch {epoch}:")
    pbar = tqdm(dataloader)
    for i, images in enumerate(pbar):
        if isinstance(images, (tuple, list)) and len(images) == 1:
            images = images[0]
        t = diffusion.sample_timesteps(images.shape[0]).to(device)
        x_t, noise = diffusion.noise_images(images, t)
        predicted_noise = model(x_t, t)
        loss = mse(noise, predicted_noise)

        optimizer.zero_grad()
        loss.backward()
        optimizer.step()

        pbar.set_postfix({'epoch': epoch, 'batch': i, 'MSE': loss.item()})
    console.print(f'epoch: {epoch}, loss: {loss.item()}')
    sampled_images = diffusion.sample(model, n=images.shape[0])
    sampled_images_history.append(sampled_images)
    sns.set_context('notebook')
    #tmp = initial_states.reshape(-1, 2, 32, 32)
    fig, ax = plt.subplots(ncols=2)
    _ = ax[0].imshow(sampled_images[0, 0, :, :])
    _ = ax[1].imshow(sampled_images[0, 1, :, :])
    _ = ax[0].set_xticklabels([])
    _ = ax[1].set_xticklabels([])
    _ = ax[0].set_yticklabels([])
    _ = ax[1].set_yticklabels([])
    _ = ax[0].set_title(r"$U_{0}$", loc='center')
    _ = ax[1].set_title(r"$U_{1}$", loc='center')
    _ = fig.suptitle('Diffusion Samples', y=0.8)
    plt.show()
    savefig(fname=f'sampled_image_epoch{epoch}', outdir=PLOTS_DIR, tstamp=True)
    MODEL_FILE = OUTDIR.joinpath("models", f"unet-diffusion-epoch{epoch}.pt")
    MODEL_FILE.parent.mkdir(exist_ok=True, parents=True)
    console.print(f"Saving model checkpoint to: {MODEL_FILE}")
    torch.save(model.state_dict(), MODEL_FILE)

Starting epoch 0:

{"model_id":"19b415c346b24bef8b60336d7f7bc355","version_major":2,"version_minor":0}

epoch: 0, loss: 0.6023472547531128

{"model_id":"eea24504754f4cb9ab4d9925a6225c10","version_major":2,"version_minor":0}

Saving sampled_image_epoch0-2023-09-21-124506 to l2hmc-diffusion-2dU1/2023-09-21/plots

Saving model checkpoint to: l2hmc-diffusion-2dU1/2023-09-21/models/unet-diffusion-epoch0.pt

<Figure size 640x480 with 0 Axes>

sns.set_context('notebook')
tmp = initial_states.reshape(-1, 2, 32, 32)
fig, ax = plt.subplots(ncols=2)
_ = ax[0].imshow(tmp[0, 0, :, :])
_ = ax[1].imshow(tmp[0, 1, :, :])
_ = ax[0].set_title(r"$U_{0}$", loc='center')
_ = ax[0].set_xticklabels([])
_ = ax[1].set_xticklabels([])
_ = ax[0].set_yticklabels([])
_ = ax[1].set_yticklabels([])
_ = ax[1].set_title(r"$U_{1}$", loc='center')
_ = fig.suptitle('HMC Samples', y=0.8)

sampled_images_history_ = torch.stack(sampled_images_history)

sampled_images_history_.shape

torch.Size([1, 5, 2, 32, 32])

sns.set_context('notebook')
fig, ax = plt.subplots(ncols=2)
_ = ax[0].imshow(sampled_images_history_[0][0][0])
_ = ax[1].imshow(sampled_images_history_[0][0][1])
_ = ax[0].set_xticklabels([])
_ = ax[1].set_xticklabels([])
_ = ax[0].set_yticklabels([])
_ = ax[1].set_yticklabels([])
_ = ax[0].set_title(r"$U_{0}$", loc='center')
_ = ax[1].set_title(r"$U_{1}$", loc='center')
_ = fig.suptitle('Diffusion Samples', y=0.85)

for idx in range(sampled_images_history_.shape[0]):
    q = exp.trainer.lattice.charges(x=sampled_images_history_[idx])
    console.print(f'{idx}: {q}')

0: Charges(intQ=tensor([ 5.0000e+00, -4.0000e+00, -6.0000e+00, -4.5535e-07,  1.0000e+00]), sinQ=tensor([ 1.6426, -1.7244, -4.4651,  0.5680,  0.7046]))

HMC Sampling with Diffusion

#for retrain_iter in range(config['retrains']):
state = exp.trainer.dynamics.random_state(config['beta'])
x = state.x

histories = {}
samples = []
hmc_samples = []
diffusion_samples = []

global_step = 0
watcher = {}
update_types = []
combined_samples = {}

global_step

for retrain_iter in range(2):
    console.print(f'retrain_iter: {retrain_iter}')
    ndiff_acc = 0
    ndiff_proposed = 0
    histories[retrain_iter] = {
        'diffusion': [],
        'hmc': [],
    }
    #for idx in range(config['samples_per_retrain']):
    sbar = tqdm(range(10))
    for idx in sbar:
        t0_ = time.perf_counter()
        if idx % 100 == 0:
            console.print(f'sample idx: {idx}')
        rand = np.random.uniform()
        if (retrain_iter >= 1) and rand < diffusion_prob:
            console.print(f'rand: {rand} < {diffusion_prob}')
            # Sample from diffusion model
            x_ = diffusion.sample(model, n=x.shape[0])
            ll_ = exp.trainer.dynamics.potential_energy(x_, config['beta'])
            ll = exp.trainer.dynamics.potential_energy(x, config['beta'])
            ratio = ll_ / ll
            a = torch.min(torch.ones_like(ratio), ratio)
            u = torch.rand(a.shape)
            #u = np.random.uniform()
            #for jdx in range(u.shape[0]):
            #    if u[jdx] < a[jdx]:
            #        samples.append(x_[jdx])
            #        diffusion_samples.append(x_[jdx])
            #x = torch.where((u < a), x_, x.reshape_as(x_)).reshape_as(x)
            x = torch.where((u < a)[:, None, None, None], x_, x.reshape_as(x_))
            samples.append(x)
            diffusion_samples.append(x)
            combined_samples[global_step] = x
            watcher[global_step] = 'diffusion'
            #diffusion_samples.extend(x)
            #samples.extend(x)
            #ndiff_acc += 
            #if u < a:
            #    console.print('Accepted diffusion sample!')
            #    console.print(f'{ndiff_acc} / {ndiff_proposed}')
            #    ndiff_acc += 1
            #    x = x_
            #    diffusion_samples.append(x)
            #    samples.append(x)
        else:
            # Oherwise, HMC
            x, metrics = exp.trainer.hmc_step((x, config['beta']))
            hmc_samples.append(x)
            samples.append(x)
            combined_samples[global_step] = x
            watcher[global_step] = 'HMC'
        smetrics = {
            'idx': idx,
            'global_step': global_step,
            'dt': time.perf_counter() - t0_,
        }
        global_step += 1
        #smetrics |= {
        #    f'{k}': {torch.tensor(v).mean().item()} for k, v in metrics.items()
        #}
        sbar.set_postfix(smetrics)
    # Train loop
    dataset = TensorDataset(
        torch.stack(hmc_samples).reshape(-1, 2, 32, 32)
    )
    dataloader = DataLoader(
        dataset,
        shuffle=False,
        drop_last=True,
        batch_size=config["train_batch_size"],
    )
    pbar = tqdm(dataloader)
    for i, batch in enumerate(pbar):
        if i == 0:
            console.print('Retraining...')
        if isinstance(batch, (tuple, list)) and len(batch) == 1:
            batch, = batch
        batch = batch.reshape(-1, 2, 32, 32)
        t0 = time.time()
        t = diffusion.sample_timesteps(batch.shape[0]).to(device)
        x_t, noise = diffusion.noise_images(batch, t)
        predicted_noise = model(x_t, t)
        loss = mse(noise, predicted_noise)
        optimizer.zero_grad()
        loss.backward()
        optimizer.step()
        t1 = time.time()
        pbar.set_postfix(
            {
                'global_step': global_step,
                'retrain_iter': retrain_iter,
                'batch': i,
                'dt': t1 - t0,
                'MSE': loss.item()
            }
        )

retrain_iter: 0

{"model_id":"17132d7ca8624fa387ee9467e4f1fa4d","version_major":2,"version_minor":0}

sample idx: 0

{"model_id":"0ed1080fdebd4f7b9aae80db0d36b96b","version_major":2,"version_minor":0}

Retraining...

retrain_iter: 1

{"model_id":"d0346019e21b4d2a9b624dc59e84015b","version_major":2,"version_minor":0}

sample idx: 0

rand: 0.05506106760134255 < 0.1

{"model_id":"c02b09d53ada46a194a47921f0ab3cba","version_major":2,"version_minor":0}

rand: 0.07860283644524213 < 0.1

{"model_id":"184df3f1c9714ece9756866b2617ed02","version_major":2,"version_minor":0}

{"model_id":"eaa0d84229c04618b7a2bffe2a4b1739","version_major":2,"version_minor":0}

Retraining...

console.print('\n'.join([f"{i.shape}" for i in samples[:100]]))

torch.Size([16, 2048])
torch.Size([16, 2048])
torch.Size([16, 2048])
torch.Size([16, 2048])
torch.Size([16, 2048])
torch.Size([16, 2048])
torch.Size([16, 2048])
torch.Size([16, 2048])
torch.Size([16, 2048])
torch.Size([16, 2048])
torch.Size([16, 2048])
torch.Size([16, 2048])
torch.Size([16, 2048])
torch.Size([16, 2048])
torch.Size([16, 2048])
torch.Size([16, 2048])
torch.Size([16, 2048])
torch.Size([16, 2048])
torch.Size([16, 2048])
torch.Size([16, 2048])
torch.Size([16, 2048])
torch.Size([16, 2048])
torch.Size([16, 2048])
torch.Size([16, 2048])
torch.Size([16, 2048])
torch.Size([16, 2048])
torch.Size([16, 2048])
torch.Size([16, 2, 32, 32])
torch.Size([16, 2048])
torch.Size([16, 2, 32, 32])

samples_ = torch.stack([i.reshape(-1, 2, 32, 32) for i in samples])
samples_.shape

torch.Size([30, 16, 2, 32, 32])

len(hmc_samples)

len(diffusion_samples)

hmc_samples_ = torch.stack([i.reshape(-1, 2, 32, 32) for i in hmc_samples])
diffusion_samples_ = torch.stack(
    [i.reshape(-1, 2, 32, 32) for i in diffusion_samples]
)

hmc_samples_.shape

torch.Size([28, 16, 2, 32, 32])

diffusion_samples_.shape

torch.Size([2, 16, 2, 32, 32])

samples_.shape

torch.Size([30, 16, 2, 32, 32])

def calc_plaqs(x):
    return torch.stack([
        exp.trainer.lattice.plaqs(
            x[:, idx]
        ) for idx in range(x.shape[1])
    ], -1)

def calc_intQ(x):
    return torch.stack([
        exp.trainer.lattice.int_charges(
            x[:, idx]
        ) for idx in range(x.shape[1])
    ], -1)
    
def calc_sinQ(x):
    return torch.stack([
        exp.trainer.lattice.sin_charges(
            x[:, idx]
        ) for idx in range(x.shape[1])
    ], -1)

samples_init_ = initial_states.reshape(-1, initial_states.shape[1], 2, 32, 32)
samples_init_.shape

torch.Size([999, 16, 2, 32, 32])

metrics_init_ = {
    'plaqs': calc_plaqs(samples_init_),
    'intQ': calc_intQ(samples_init_),
    'sinQ': calc_sinQ(samples_init_)
}
    
metrics_ = {
    'plaqs': calc_plaqs(samples_),
    'intQ': calc_intQ(samples_),
    'sinQ': calc_sinQ(samples_)
}

metrics_hmc_ = {
    'plaqs': calc_plaqs(hmc_samples_),
    'intQ': calc_intQ(hmc_samples_),
    'sinQ': calc_sinQ(hmc_samples_)
}

metrics_diffusion_ = {
    'plaqs': calc_plaqs(diffusion_samples_),
    'intQ': calc_intQ(diffusion_samples_),
    'sinQ': calc_sinQ(diffusion_samples_)
}

metrics_['plaqs'].shape

torch.Size([30, 16])

console.print('\n'.join([f"{k}: {v}" for k, v in watcher.items()]))

0: HMC
1: HMC
2: HMC
3: HMC
4: HMC
5: HMC
6: HMC
7: HMC
8: HMC
9: HMC
10: HMC
11: HMC
12: HMC
13: HMC
14: HMC
15: HMC
16: HMC
17: HMC
18: HMC
19: HMC
20: HMC
21: HMC
22: HMC
23: HMC
24: HMC
25: HMC
26: HMC
27: diffusion
28: HMC
29: diffusion

fig, ax = plt.subplots()

_ = ax.plot(metrics_['plaqs'][:, 0], label='Combined')
_ = ax.plot(metrics_hmc_['plaqs'][:, 0], label='HMC')
_ = ax.plot(metrics_diffusion_['plaqs'][:, 0], label='Diffusion')
#_ = ax.plot(metrics_hmc1['plaqs'], label='HMC 1')
#_ = ax.plot(metrics_diff_['plaqs'], label='Diffusion')
_ = ax.legend(loc='upper left', bbox_to_anchor=(1.05, 1.00))

fig, ax = plt.subplots(ncols=3, figsize=(14, 4))
for idx, (key, val) in enumerate(metrics_init_.items()):
    _ = ax[idx].plot(val[:, 0], label='HMC (Initial Samples)')
    _ = ax[idx].set_ylabel(key, loc='center')
    _ = ax[idx].set_xlabel('Draw', loc='center')
    #_ = ax[idx].legend(loc='best', frameon=True, edgecolor="#838383")

_ = fig.suptitle(f"Initial HMC States", y=0.92)

fig, ax = plt.subplots(ncols=3, figsize=(14, 4))
for idx, (key, val) in enumerate(metrics_.items()):
    _ = ax[idx].plot(val[:, 0], label='Combined')
    _ = ax[idx].set_ylabel(key, loc='center')
    _ = ax[idx].set_xlabel('Draw', loc='center')
    #_ = ax[idx].legend(loc='best', frameon=True, edgecolor="#838383")

_ = fig.suptitle(f"Combined Samples", y=0.92)

fig, ax = plt.subplots(ncols=3, figsize=(14, 4))
for idx, (key, val) in enumerate(metrics_hmc_.items()):
    _ = ax[idx].plot(val[:, 0], label='HMC')
    _ = ax[idx].set_ylabel(key, loc='center')
    _ = ax[idx].set_xlabel('Draw', loc='center')
_ = fig.suptitle(f"Generated HMC States", y=0.92)

fig, ax = plt.subplots(ncols=3, figsize=(14, 4))
for idx, (key, val) in enumerate(metrics_diffusion_.items()):
    _ = ax[idx].plot(val[:, 0], label='Diffusion')
    _ = ax[idx].set_ylabel(key, loc='center')
    _ = ax[idx].set_xlabel('Draw', loc='center')
_ = fig.suptitle(f"Generated Diffusion States", y=0.92)

from l2hmc.lattice.u1.pytorch.lattice import plaq_exact
plaq_exact(torch.tensor(6.0))

tensor(0.9124)

fig, ax = plt.subplots()
#_ = plt.hist(metrics_['intQ'].flatten(), color='C0', alpha=0.6, label='Combined', edgecolor='none')
_ = ax.hist(
    metrics_diffusion_['intQ'].flatten(),
    color='C0',
    alpha=0.6,
    edgecolor='none',
    label='Diffusion',
    density=True,
)
_ = ax.hist(
    metrics_hmc_['intQ'].flatten(),
    color='C1',
    alpha=0.6,
    edgecolor='none',
    label='HMC',
    density=True,
)
_ = ax.legend(loc='best', frameon=True, edgecolor='#666666')
_ = ax.set_xlabel(r"$Q$", loc='center')
_ = ax.set_title('Topological Charge ($Q$) Distribution', loc='center')

fig, ax = plt.subplots()
_ = plt.plot(metrics_['plaqs'][:, 0], color='C0', label='Diffusion')
_ = plt.plot(metrics_hmc_['plaqs'][:, 0], color='C1', label='HMC')
_ = ax.legend(loc='best', frameon=True, edgecolor='#666666', ncols=2)
_ = ax.set_ylabel(r"$\left\langle U_{\mu\nu}\right\rangle $", loc='center')
_ = ax.set_xlabel(f"Draw", loc='center')

wloops = {
    'hmc': [
        exp.trainer.lattice.wilson_loops(i) for i in hmc_samples_
    ],
    'diffusion': [
        exp.trainer.lattice.wilson_loops(i) for i in diffusion_samples_
    ],
}

plaqs = {
    'hmc': [
        exp.trainer.lattice.plaqs(i) for i in hmc_samples_
    ],
    'diffusion': [
        exp.trainer.lattice.plaqs(i) for i in diffusion_samples_
    ],
}

wlhmc = torch.stack(wloops['hmc']).squeeze()
wldiff = torch.stack(wloops['diffusion']).squeeze()

wlhmc.shape

torch.Size([28, 16, 32, 32])

_ = plt.tight_layout()
for idx in range(2):
    fig, ax = plt.subplots(ncols=2)
    _ = ax[0].imshow(wlhmc[idx, 0])
    _ = ax[0].set_title("HMC", loc='center')
    _ = ax[1].imshow(wldiff[idx, 0])
    _ = ax[1].set_title("Diffusion", loc='center')
    _ = fig.suptitle(r"$U_{\mu\nu}$", y=0.8)
    for ax_ in ax:
        _ = ax_.set_xticklabels([])
        _ = ax_.set_yticklabels([])

<Figure size 640x480 with 0 Axes>

qhmc = metrics_hmc_['intQ']
qdiff = metrics_diffusion_['intQ']
qhmc.shape

torch.Size([28, 16])

phmc = torch.stack(plaqs['hmc']).squeeze()
pdiff = torch.stack(plaqs['diffusion']).squeeze()
phmc.shape

torch.Size([28, 16])

pdiff.shape

torch.Size([2, 16])

fig, ax = plt.subplots()

_ = ax.hist(
    metrics_['plaqs'].flatten(),
    color='C1',
    histtype='step',
    stacked=True,
    density=True,
    label='HMC',
    linewidth=1.5
)
_ = ax.hist(
    metrics_diffusion_['plaqs'].flatten(),
    color='C0',
    histtype='step',
    stacked=True,
    density=True,
    label='Diffusion',
    linewidth=1.5
)
_ = ax.hist(
    metrics_hmc_['plaqs'].flatten(),
    color='C2',
    histtype='step',
    stacked=True,
    density=True,
    label='Combined',
    linewidth=1.5
)
_ = ax.set_xlabel(r"$U_{\mu\nu}$", loc='center')
_ = ax.legend(
    loc='upper left',
    frameon=True,
    #ncols=2,
    bbox_to_anchor=(0.55, 1.00),
    edgecolor="#838383",
)
_ = ax.set_title('Plaquette Distribution', loc='center')

fig, ax = plt.subplots()

_ = ax.hist(
    metrics_['intQ'].flatten(),
    color='C1',
    histtype='step',
    stacked=True,
    density=True,
    label='HMC',
    linewidth=1.5
)
_ = ax.hist(
    metrics_diffusion_['intQ'].flatten(),
    color='C0',
    histtype='step',
    stacked=True,
    density=True,
    label='Diffusion',
    linewidth=1.5
)
_ = ax.hist(
    metrics_hmc_['intQ'].flatten(),
    color='C2',
    histtype='step',
    stacked=True,
    density=True,
    label='Combined',
    linewidth=1.5
)
_ = ax.set_xlabel('$Q_{\mathbb{Z}}$', loc='center')
_ = ax.legend(
    loc='upper left',
    frameon=True,
    #ncols=2,
    bbox_to_anchor=(0.55, 1.00),
    edgecolor="#838383",
)
_ = ax.set_title('Charge Distribution', loc='center')

global_step = 0
frames = []
losses = []
print("Training model...")
for epoch in range(config["num_epochs"]):
    model.train()
    progress_bar = tqdm(total=len(dataloader))
    progress_bar.set_description(f"Epoch {epoch}")
    for step, batch in enumerate(dataloader):
        t = diffusion.sample_timesteps(images.shape[0]).to(device)

        noise = torch.randn(batch.shape)
        timesteps = torch.randint(
            0, noise_scheduler.num_timesteps, (batch.shape[0],)
        ).long()

        #noisy = noise_scheduler.add_noise(batch, noise, timesteps)
        noisy = noise_scheduler.noise_images(batch, timesteps)
        noise_pred = model(noisy, timesteps)
        loss = F.mse_loss(noise_pred, noise)
        loss.backward(loss)

        nn.utils.clip_grad_norm_(model.parameters(), 1.0)
        optimizer.step()
        optimizer.zero_grad()

        progress_bar.update(1)
        logs = {"loss": loss.detach().item(), "step": global_step}
        losses.append(loss.detach().item())
        progress_bar.set_postfix(**logs)
        global_step += 1
    progress_bar.close()

    if epoch % config["save_images_step"] == 0 or epoch == config["num_epochs"] - 1:
        # generate data with the model to later visualize the learning process
        model.eval()
        sample = torch.randn(config["eval_batch_size"], 2)
        timesteps = list(range(len(noise_scheduler)))[::-1]
        for i, t in enumerate(tqdm(timesteps)):
            t = torch.from_numpy(np.repeat(t, config["eval_batch_size"])).long()
            with torch.no_grad():
                residual = model(sample, t)
            sample = noise_scheduler.step(residual, t[0], sample)
        frames.append(sample.numpy())

dataset[6]

len(dataloader)

eval_batch_size = 10
num_timesteps = 50
plot_step = 5
noise_scheduler = ddpm.NoiseScheduler(num_timesteps=num_timesteps)
sample = torch.randn(eval_batch_size, 2)
timesteps = list(range(num_timesteps))[::-1]
samples = []
steps = []

retrains = 10
diffusion_prob = 0.3
samples_per_retrain = 100

eval_batch_size = 10
t = torch.from_numpy(np.repeat(timesteps[0], eval_batch_size)).long()
with torch.no_grad():
    residual = model(sample, t)
sample_ = noise_scheduler.step(residual, t[0], sample)

sample.shape

residual.shape

sample_.shape

diffusion_samples = []
hmc_samples = []
beta = 1.
for retrain_iter in range(retrains):
    console.print(f'retrain_iter: {retrain_iter}')
    ndiff_acc = 0
    ndiff_proposed = 0
    for idx in range(samples_per_retrain):
        console.print(f'sample idx: {idx}')
        rand = np.random.uniform()
        if rand < diffusion_prob:
            ndiff_proposed += 1
            rand_pick = randrange(len(dataloader))
            #theta_prime = dataset[rand_pick]
            t = torch.from_numpy(np.repeat(t, eval_batch_size)).long()
            with torch.no_grad():
                residual = model(sample, t)
            sample_ = noise_scheduler.step(residual, t[0], sample)
            ratio = (
                log_likelihood_2dU1(sample_, 2)
                / log_likelihood_2dU1(sample, 2)
            )
            a = min(1, ratio)
            u = np.random.uniform()
            if u < a:
                ndiff_acc += 1
                sample = sample_
                diffusion_samples.append(sample)
        else:
            sample_, metrics = exp.trainer.hmc_step((sample_, beta))
            hmc_samples.append(sample)

for i, t in enumerate(tqdm(timesteps)):
    t = torch.from_numpy(np.repeat(t, eval_batch_size)).long()
    with torch.no_grad():
        residual = model(sample, t)
    sample = noise_scheduler.step(residual, t[0], sample)
    if (i + 1) % plot_step == 0:
        samples.append(sample.numpy())
        steps.append(i + 1)

Alternate

diffusion_ = DiffusionAlt(img_size=64, device='cpu')

unet

image = torch.rand(1, 2, 64, 64)
t = diffusion_.sample_timesteps(image.shape[0]).to('cpu')
unet(image, t)

diffusion_.sample(

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Citation

BibTeX citation:

@online{foreman2024,
  author = {Foreman, Sam},
  title = {MCMC + {Diffusion} {Sampling}},
  date = {2024-04-15},
  url = {https://samforeman.me/qmd/l2hmc-qcd/diffusion},
  langid = {en}
}

For attribution, please cite this work as:

Foreman, Sam. 2024. “MCMC + Diffusion Sampling.” April 15, 2024. https://samforeman.me/qmd/l2hmc-qcd/diffusion.