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diff --git a/notebooks/mnist_example/MNIST_Diffusion_Example.ipynb b/notebooks/mnist_example/MNIST_Diffusion_Example.ipynb
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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# This notebook demonstrates how to train a score-based diffusion model on the MNIST dataset. \n",
+    "\n",
+    "We will introduce MNIST, show how to download the dataset, train a score-based diffusion model on MNSIT, and evaluate the quality of the samples generated by our trained modelusing the [PQMass](https://arxiv.org/abs/2402.04355) metric, introduced by Lemos et al. (2024)."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {
+    "tags": [
+     "hide-input"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "# General Imports \n",
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "import torch\n",
+    "import torchvision.transforms as transforms\n",
+    "from torchvision.datasets import MNIST\n",
+    "import os \n",
+    "\n",
+    "# Imports for Score Model\n",
+    "from score_models import ScoreModel, EnergyModel, NCSNpp, MLP, DDPM\n",
+    "\n",
+    "# Imports for PQMass\n",
+    "from scipy.stats import norm, chi2, uniform\n",
+    "from pqm import pqm_chi2\n",
+    "\n",
+    "# Imports for Nice Plotting\n",
+    "import matplotlib as mpl\n",
+    "mpl.rcParams['figure.dpi'] = 200\n",
+    "plt.rc(\"font\", **{\"family\": \"serif\", \"serif\": [\"Computer Modern\"]})\n",
+    "plt.rc(\"text\", usetex=True)\n",
+    "\n",
+    "# Create a Folder called MNIST_Checkpoint_Directory if it doesn't exist - This is used during training the diffusion model\n",
+    "# Define the directory path\n",
+    "checkpoint_dir = './MNIST_Checkpoint_Directory'\n",
+    "\n",
+    "# Check if the directory exists, and if not, create it\n",
+    "if not os.path.exists(checkpoint_dir):\n",
+    "    os.makedirs(checkpoint_dir)\n",
+    "\n",
+    "device = torch.device(\"cuda:0\" if torch.cuda.is_available() else \"cpu\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# MNIST\n",
+    "\n",
+    "The data we are going to be working with is called MNIST. It is a 60,000 training and 10,000 test images of handwritten digits from 0 to 9. All the images are grayscaled, meaning one channel, and each image is 28x28 pixels. It is widely used for benchmarking machine learning models due to its simplicity and ease of visualization."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def open_data(data_dir, num_samples=10000, train=True):\n",
+    "    # Define the transform to convert images to tensors\n",
+    "    transform = transforms.Compose([transforms.ToTensor()])\n",
+    "    \n",
+    "    # Load the MNIST dataset with the transform applied\n",
+    "    all_mnist = MNIST(data_dir, train=train, transform=transform, download=False)\n",
+    "    \n",
+    "    # Randomly select a subset of images\n",
+    "    total_samples = len(all_mnist)\n",
+    "    random_indices = torch.randperm(total_samples)[:num_samples]\n",
+    "    \n",
+    "    # Stack only the selected images\n",
+    "    dataset = torch.stack([all_mnist[i][0] for i in random_indices], dim=0)\n",
+    "\n",
+    "    return dataset\n",
+    "\n",
+    "class MNIST_datasets(torch.utils.data.Dataset):\n",
+    "    def __init__(self, data_dir, *args, num_samples=10000):\n",
+    "        self.args = args\n",
+    "        # Load training and test datasets\n",
+    "        self.dataset = open_data(data_dir=data_dir, num_samples=num_samples, train=True)\n",
+    "        self.dataset_test = open_data(data_dir=data_dir, num_samples=num_samples, train=False)\n",
+    "\n",
+    "    def __len__(self):\n",
+    "        return len(self.dataset)\n",
+    "\n",
+    "    def __getitem__(self, idx):\n",
+    "        data = []\n",
+    "        for i in range(1, len(self.datasets) + 1):\n",
+    "            data.append(self.datasets[f'dataset{i}'][idx].to(device))\n",
+    "\n",
+    "        return data\n",
+    "    \n",
+    "# Set the data directory\n",
+    "data_dir = './data'\n",
+    "\n",
+    "# Download MNIST\n",
+    "MNIST(data_dir, train=True, download=True, transform=transforms.ToTensor())\n",
+    "MNIST(data_dir, train=False, download=True, transform=transforms.ToTensor())\n",
+    "\n",
+    "# Initialize the mult_datasets instance\n",
+    "dataset_instance = MNIST_datasets(data_dir=data_dir)\n",
+    "\n",
+    "# Access both train and test datasets\n",
+    "train_data = dataset_instance.dataset\n",
+    "test_data = dataset_instance.dataset_test"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Diffusion Model Setup\n",
+    "\n",
+    "Here we define the setup for a diffusion model such that it can be trained on all 60k MNIST grayscaled images. This is just an example of the hyperparameters and leave it for the reader to modify the hyperparameters as they see fit."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Using the Variance Preserving SDE\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Epoch 10 | Cost: 1.8e+01 |: 100%|██████████| 10/10 [02:07<00:00, 12.78s/it]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Finished training after 0.035 hours.\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "[162.28086529502386,\n",
+       " 38.11480836023258,\n",
+       " 27.26716512366186,\n",
+       " 23.280498987511745,\n",
+       " 20.737696273417413,\n",
+       " 19.808246214178546,\n",
+       " 19.183665178999117,\n",
+       " 18.101966061169588,\n",
+       " 18.22634054739264,\n",
+       " 18.268924833853035]"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "checkpoints_directory = './MNIST_Checkpoint_Directory'\n",
+    "\n",
+    "net = NCSNpp(channels=1, dimensions=2, nf=128, ch_mult=[2, 2])\n",
+    "model = ScoreModel(model=net, beta_min=1e-2, beta_max=20).to(device)\n",
+    "\n",
+    "model.fit(train_data.to(device), epochs=10, batch_size=128, learning_rate=1e-3, ema_decay = 0.999,\n",
+    "                   checkpoints_directory=checkpoints_directory)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Sampling\n",
+    "\n",
+    "Now we have trained our model, we can generate samples and see what our model has learned"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Sampling from the prior | t = 0.0 | sigma = 4.5e-03| scale ~ 2.9e-01: 100%|██████████| 1000/1000 [00:10<00:00, 99.07it/s]\n"
+     ]
+    }
+   ],
+   "source": [
+    "model.eval()\n",
+    "\n",
+    "B = 10 # Number of samples you want to generate\n",
+    "dimensions = [1, 28, 28] # The spatial dimensions of MNIST; 1 channel (black and white), 28x28 pixels\n",
+    "\n",
+    "# Generate samples from the trained model (steps is the number of Euler-Maruyama steps)\n",
+    "samples = model.sample(shape=[B, *dimensions], steps=1000)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {
+    "tags": [
+     "hide-cell",
+     "hide-input"
+    ]
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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+      "text/plain": [
+       "<Figure size 4000x1200 with 20 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# Define the number of images you want to plot\n",
+    "B = 10\n",
+    "\n",
+    "# Create a 2xB grid of subplots\n",
+    "fig, ax = plt.subplots(2, B, figsize=(20, 6))\n",
+    "\n",
+    "# Plot the model's samples in the first row\n",
+    "for i in range(B):\n",
+    "    ax[0, i].imshow(samples[i, 0].cpu().detach().numpy(), cmap='gray')\n",
+    "    ax[0, i].axis('off')\n",
+    "\n",
+    "# Plot the test images in the second row\n",
+    "for i in range(B):\n",
+    "    ax[1, i].imshow(test_data[i, 0].cpu().detach().numpy(), cmap='gray')\n",
+    "    ax[1, i].axis('off')\n",
+    "\n",
+    "# Add row titles\n",
+    "fig.text(0.5, 0.92, 'Samples from Diffusion Model at Epoch 10', ha='center', fontsize=30)\n",
+    "fig.text(0.5, 0.48, 'Test Set from MNIST', ha='center', fontsize=30)\n",
+    "\n",
+    "# Adjust spacing between subplots for better layout\n",
+    "plt.tight_layout()\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Do these samples come from the same distribution as the test set? Has it learned the underlying distribution? How can you tell? There are statistical methods to evaluate if the samples come from the same distribution such as [PQMass](https://arxiv.org/abs/2402.04355). This gives you a way of determining if the distrubution your model has learned is similar a test/validation distribution. In this case we use to compare the samples our model generatives to the test set of MNIST!\n",
+    "\n",
+    "You need a lot of samples so we will load in 5k samples that have already been generated to show how PQMass works. Note that this is is the model with the same hyperparameters trained offline for 100 epochs that is in the folder."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Samples from a pretrained model at Epoch 100 (can be found in here (link)) \n",
+    "samples = torch.load('./Epoch_100_MNIST_1000_Samples_VP_NF_128_Ch_Mult_2_2_Batch_Size_128_LR_1e_3_ema_decay_0_999.pt', weights_only=False)\n",
+    "samples = samples.unsqueeze(1)  # Adds the channel dimension"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We plot the samples to show what they look like verus the test set of MNIST. (Note that this is not the same epoch as from above so these samples look much better!)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {
+    "tags": [
+     "hide-cell",
+     "hide-input"
+    ]
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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+      "text/plain": [
+       "<Figure size 4000x1200 with 20 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# Define the number of images you want to plot\n",
+    "B = 10\n",
+    "\n",
+    "# Create a 2xB grid of subplots\n",
+    "fig, ax = plt.subplots(2, B, figsize=(20, 6))\n",
+    "\n",
+    "# Plot the model's samples in the first row\n",
+    "for i in range(B):\n",
+    "    ax[0, i].imshow(samples[i, 0].cpu().detach().numpy(), cmap='gray')\n",
+    "    ax[0, i].axis('off')\n",
+    "\n",
+    "# Plot the test images in the second row\n",
+    "for i in range(B):\n",
+    "    ax[1, i].imshow(test_data[i, 0].cpu().detach().numpy(), cmap='gray')\n",
+    "    ax[1, i].axis('off')\n",
+    "\n",
+    "# Add row titles\n",
+    "fig.text(0.5, 0.92, 'Samples from Diffusion Model at Epoch 100', ha='center', fontsize=30)\n",
+    "fig.text(0.5, 0.48, 'Test Set from MNIST', ha='center', fontsize=30)\n",
+    "\n",
+    "# Adjust spacing between subplots for better layout\n",
+    "plt.tight_layout()\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Normalize with respect to test_images as that is what we are comparing to\n",
+    "normalized_normalized_test_data = ((test_data - torch.min(test_data)) / (torch.max(test_data) - torch.min(test_data))) \n",
+    "normalized_samples = ((samples - torch.min(test_data)) / (torch.max(test_data) - torch.min(test_data))) \n",
+    "\n",
+    "# Reshape\n",
+    "normalized_samples = normalized_samples.data.reshape(-1, 28*28)\n",
+    "normalized_normalized_test_data = normalized_normalized_test_data.data.reshape(-1, 28*28)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# PQMass\n",
+    "\n",
+    "The way PQMass works is that given two distributions, $p$ and $q$, it randomly selects reference points from each dataset. Then it constructs $n_R$ Voronoi tesellations around those centers. Then based on the distribution of each dataset, the number of samples in a given region is counted. It follows that any given sample follows a Multinomial distribution, it can be in region A or any other region, in which the PQMass paper constructed a way to evaluate both a $\\chi^2$ metric and a p-value to measure if the $p$ and $q$ come from the same distribution or not. For this notebook we use the $\\chi^2$ metric."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "99.04893425663707 11.433193566118554\n"
+     ]
+    }
+   ],
+   "source": [
+    "zs = []\n",
+    "num_repeats = 35\n",
+    "n = len(samples) // num_repeats\n",
+    "m = len(test_data) // num_repeats\n",
+    "\n",
+    "for i in range(num_repeats):\n",
+    "    for _ in range(num_repeats):\n",
+    "        z = pqm_chi2(normalized_samples[i*n:(i+1)*n].cpu(), normalized_normalized_test_data[i*m:(i+1)*m].cpu())\n",
+    "        zs.append(z)\n",
+    "\n",
+    "print(np.median(zs), np.std(zs))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Above we show the median and the standard deviation but if you want to see another way of showcasing how in or out of distribution your samples are, you can plot them against the $\\chi^2$ distribution. You want your samples (blue) to match the test distribuition (red). We show that the generated samples are well in distribution with the test set from MNIST meaning our model has learned the correct underlying distrubution!"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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+      "text/plain": [
+       "<Figure size 1200x700 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig, ax = plt.subplots(figsize=(6, 3.5))\n",
+    "ax.hist(zs, bins=10, density=True)\n",
+    "ax.plot(np.linspace(60, 160, 100), chi2.pdf(np.linspace(60, 160, 100), df=99), color='red')\n",
+    "ax.set_xlabel(r'$\\chi^2_{{\\rm PQM}}$')\n",
+    "ax.set_ylabel('Frequency')\n",
+    "plt.title('MNIST Test Set vs Samples from NCSN++ model')\n",
+    "plt.tight_layout()\n",
+    "plt.show()"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "tarp_project",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.9.18"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/notebooks/mnist_example/checkpoint_1.1605e+01_100.pt b/notebooks/mnist_example/checkpoint_1.1605e+01_100.pt
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index 0000000..0db46cc
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