Upload flowmatching.ipynb

Pytorch implementation of flow matching for generative modeling on simple 2d sampling points. Amazing walkthrough video by Outlier

flowmatching.ipynb

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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
+}