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"cells": [
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"#creating a simple sample of points\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import math\n",
"import tqdm\n",
"import torch\n",
"from torch import nn\n",
"from matplotlib.colors import ListedColormap\n",
"\n",
"N = 1000 #number of points to sample\n",
"x_min, x_max = -4, 4\n",
"y_min, y_max = -4, 4\n",
"resolution = 100 #resolution of the grid\n",
"\n",
"x = np.linspace(x_min, x_max, resolution)\n",
"y = np.linspace(y_min, y_max, resolution)\n",
"X, Y = np.meshgrid(x, y)\n",
"\n",
"length = 4\n",
"checkerboard = np.indices((length, length)).sum(axis=0) % 2\n",
"\n",
"sampled_points = []\n",
"while len(sampled_points) < N:\n",
" x_sample = np.random.uniform(x_min, x_max)\n",
" y_sample = np.random.uniform(y_min, y_max)\n",
"\n",
" i = int((x_sample - x_min) / (x_max - x_min) * length)\n",
" j = int((y_sample - y_min) / (y_max - y_min) * length)\n",
"\n",
" if checkerboard[j, i] == 1:\n",
" sampled_points.append((x_sample, y_sample))\n",
"sampled_points = np.array(sampled_points) #sampled points is our x1"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"t = 0.5\n",
"noise = np.random.randn(N, 2)\n",
"plt.figure(figsize=(6, 6))\n",
"plt.scatter(sampled_points[:, 0], sampled_points[:, 1], color=\"red\", marker=\"o\")\n",
"plt.scatter(noise[:, 0], noise[:, 1], color=\"blue\", marker=\"o\")\n",
"plt.scatter((1 - t) * noise[:, 0] + t * sampled_points[:, 0], (1 - t) * noise[:, 1] + t * sampled_points[:, 1], color=\"green\", marker=\"o\")\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"#Model\n",
"class Block(nn.Module):\n",
" def __init__(self, channels=512):\n",
" super().__init__()\n",
" self.ff = nn.Linear(channels, channels)\n",
" self.act = nn.ReLU()\n",
"\n",
" def forward(self, x):\n",
" return self.act(self.ff(x))\n",
"\n",
"class MLP(nn.Module):\n",
" def __init__(self, channels_data=2, layers=5, channels=512, channels_t=512):\n",
" super().__init__()\n",
" self.channels_t = channels_t\n",
" self.in_projection = nn.Linear(channels_data, channels)\n",
" self.t_projection = nn.Linear(channels_t, channels)\n",
" self.blocks = nn.Sequential(*[\n",
" Block(channels) for _ in range(layers)\n",
" ])\n",
" self.out_projection = nn.Linear(channels, channels_data)\n",
"\n",
" def gen_t_embedding(self, t, max_positions=10000):\n",
" t = t * max_positions\n",
" half_dim = self.channels_t // 2\n",
" emb = math.log(max_positions) / (half_dim - 1)\n",
" emb = torch.arange(half_dim, device=t.device).float().mul(-emb).exp()\n",
" emb = t[:, None] * emb[None, :]\n",
" emb = torch.cat([emb.sin(), emb.cos()], dim=1)\n",
" if self.channels_t % 2 == 1: # zero pad\n",
" emb = nn.functional.pad(emb, (0, 1), mode='constant')\n",
" return emb\n",
"\n",
" def forward(self, x, t):\n",
" x = self.in_projection(x)\n",
" t = self.gen_t_embedding(t)\n",
" t = self.t_projection(t)\n",
" x = x + t \n",
" x = self.blocks(x)\n",
" x = self.out_projection(x)\n",
" return x"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"model = MLP(layers=5, channels=512)\n",
"optim = torch.optim.AdamW(model.parameters(), lr=1e-4)\n",
"\n",
"data = torch.Tensor(sampled_points)\n",
"training_steps = 100_000\n",
"batch_size = 64\n",
"pbar = tqdm.tqdm(range(training_steps))\n",
"losses = []\n",
"for i in pbar:\n",
" x1 = data[torch.randint(data.size(0), (batch_size,))]\n",
" x0 = torch.randn_like(x1)\n",
" target = x1 - x0\n",
" t = torch.rand(x1.size(0))\n",
" xt = (1 - t[:, None]) * x0 + t[:, None] * x1\n",
" pred = model(xt, t) # also add t here\n",
" loss = ((target - pred)**2).mean()\n",
" loss.backward()\n",
" optim.step()\n",
" optim.zero_grad()\n",
" pbar.set_postfix(loss=loss.item())\n",
" losses.append(loss.item())"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"#Sampling\n",
"torch.manual_seed(42)\n",
"model.eval().requires_grad_(False)\n",
"### from here\n",
"xt = torch.randn(1000, 2)\n",
"steps = 1000\n",
"plot_every = 100\n",
"for i, t in enumerate(torch.linspace(0, 1, steps), start=1):\n",
" pred = model(xt, t.expand(xt.size(0)))\n",
" xt = xt + (1 / steps) * pred\n",
"## to here, this is the sampling logic, and it in this case its moving random noise points into an organized checkerboard\n",
"##BUT, this sampling is literally applied anywhere from images to videos, because the goal is to move each noise sample to the specific location and modification\n",
" if i % plot_every == 0:\n",
" plt.figure(figsize=(6, 6))\n",
" plt.scatter(sampled_points[:, 0], sampled_points[:, 1], color=\"red\", marker=\"o\")\n",
" plt.scatter(xt[:, 0], xt[:, 1], color=\"green\", marker=\"o\")\n",
" plt.show()\n",
"model.train().requires_grad_(True)"
]
}
],
"metadata": {
"language_info": {
"name": "python"
},
"orig_nbformat": 4
},
"nbformat": 4,
"nbformat_minor": 2
}
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