{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"background-color: #f5f5f5; padding: 20px; border-radius: 10px; border: 1px solid #e0e0e0; text-align: center;\">\n",
    "  \n",
    "  <img src=\"https://i.ibb.co/mLyt3rk/SUT-Logo.png\" alt=\"SUT Logo\" width=\"100\">\n",
    "  \n",
    "  <h1 style=\"margin:10px 0 0 0; color:#333;\">Sharif University of Technology</h1>\n",
    "  <h2 style=\"margin:0; color:#555; font-weight:normal;\">Faculty of Mathematical Sciences</h2>\n",
    "  \n",
    "  <hr style=\"border: 1px solid #ccc; margin-top:15px; margin-bottom:15px;\">\n",
    "  \n",
    "  <h3 style=\"margin:10px 0 5px 0; color:#0056b3;\">HW4: Denoising Diffusion Models</h3>\n",
    "  <h4 style=\"margin:10px 0 5px 0; color:#0056b3;\">Prepared by: Sara Karimi</h4>\n",
    "  <br/>\n",
    "  \n",
    "  <div style=\"font-size: 1.1em; color: #333; line-height: 1.6;\">\n",
    "    <strong>Course:</strong> Generative Models<br>\n",
    "    <strong>Instructor:</strong> Dr. Fatemeh Seyyedsalehi<br>\n",
    "    <strong>Semester:</strong> Fall 1404-1405\n",
    "  </div>\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"background-color: #f5f5f5; border: 1px solid #f5f5f5; padding: 20px; border-radius: 10px; margin-top: 25px; margin-bottom: 25px;\">\n",
    "  \n",
    "  <h3 style=\"text-align: center; margin-top: 0; color: #0056b3;\">Student Information</h3>\n",
    "  <p style=\"text-align: center; color: #555; margin-bottom: 20px; margin-top: 0;\">\n",
    "    Please fill in your details below.\n",
    "  </p>\n",
    "\n",
    "  <table style=\"width: 60%; margin-left: auto; margin-right: auto; border: none; font-size: 1.1em; color: #333;\">\n",
    "    <tbody>\n",
    "      <tr>\n",
    "        <td style=\"text-align: right; padding: 8px; width: 35%;\"><strong>Student Name:</strong></td>\n",
    "        <td style=\"text-align: left; padding: 8px;\"><em>Your Name Here</em></td> <!-- UPDATE THIS LINE -->\n",
    "      </tr>\n",
    "      <tr>\n",
    "        <td style=\"text-align: right; padding: 8px;\"><strong>Student ID:</strong></td>\n",
    "        <td style=\"text-align: left; padding: 8px;\"><em>Your Student ID Here</em></td>  <!-- UPDATE THIS LINE -->\n",
    "      </tr>\n",
    "    </tbody>\n",
    "  </table>\n",
    "  \n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# **HW4-P2: Human Motion Diffusion Model (MDM)**\n",
    "\n",
    "---\n",
    "\n",
    "**Assignment Overview:**\n",
    "\n",
    "In this homework, you will implement and analyze key components of the **Human Motion Diffusion Model (MDM)**, a state-of-the-art generative model for synthesizing realistic human motion sequences. This assignment combines theoretical derivations with hands-on implementation, culminating in the generation of motion sequences visualized as animated GIFs.\n",
    "\n",
    "<br/>\n",
    "\n",
    "> **Submission Note:** If the file size of your notebook becomes too large and you struggle to upload the final ZIP file to Quera, you may upload your solution to Colab or Kaggle instead. In this case, please include a `.txt` file in your Quera submission containing a link to your notebook (ensure the link settings allow anyone with the link to view it)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## Part 0: Environment Setup (0 points)\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Install required packages\n",
    "!pip install -q torch torchvision torchaudio\n",
    "!pip install -q matplotlib numpy scipy tqdm\n",
    "!pip install -q imageio[ffmpeg] Pillow\n",
    "!pip install -q einops"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.nn.functional as F\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "import imageio\n",
    "from tqdm import tqdm\n",
    "import math\n",
    "from typing import Optional, Tuple, List\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')\n",
    "print(f\"Using device: {device}\")\n",
    "\n",
    "torch.manual_seed(42)\n",
    "np.random.seed(42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## Part 1: Theoretical Foundations (15 points)\n",
    "---\n",
    "\n",
    "Before implementing MDM, we need to establish the theoretical framework. Answer the following questions with detailed derivations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 1.1: Motion Representation (5 points)\n",
    "\n",
    "Human motion in MDM is represented as a sequence $\\mathbf{x}^{1:N} = \\{\\mathbf{x}^1, \\mathbf{x}^2, ..., \\mathbf{x}^N\\}$ where each frame $\\mathbf{x}^i \\in \\mathbb{R}^{J \\times D}$ contains $J$ joints with $D$-dimensional features.\n",
    "\n",
    "The HumanML3D dataset uses a specific motion representation with $D=263$ features per frame. Research and explain what these 263 dimensions encode. Specifically:\n",
    "- Root joint features (position, orientation, velocity)\n",
    "- Joint rotation representations\n",
    "- Joint position representations\n",
    "- Foot contact labels\n",
    "\n",
    "**Part A:** Why does MDM predict the clean sample $\\hat{\\mathbf{x}}_0$ directly instead of predicting the noise $\\epsilon$ like standard DDPM? Discuss how this design choice enables the use of geometric losses.\n",
    "\n",
    "*Write your answer in the cell below:*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Your Answer:**\n",
    "\n",
    "\n",
    "**Part A:**\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 1.2: Classifier-Free Guidance (10 points)\n",
    "\n",
    "MDM uses classifier-free guidance for conditional generation. During training, the conditioning signal $c$ (text or action) is randomly masked with probability $p_{uncond}$.\n",
    "\n",
    "**Part A:** Derive the classifier-free guidance sampling formula:\n",
    "$$\\tilde{\\epsilon}_\\theta(\\mathbf{x}_t, t, c) = (1 + w) \\cdot \\epsilon_\\theta(\\mathbf{x}_t, t, c) - w \\cdot \\epsilon_\\theta(\\mathbf{x}_t, t, \\emptyset)$$\n",
    "\n",
    "starting from the score function relationship. Explain the role of guidance scale $w$.\n",
    "\n",
    "**Part B:** Since MDM predicts $\\hat{\\mathbf{x}}_0$ instead of $\\epsilon$, rewrite the classifier-free guidance formula in terms of sample predictions. Show the equivalence.\n",
    "\n",
    "\n",
    "*Write your derivations and analysis below:*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Your Answer:**\n",
    "\n",
    "\n",
    "**Part A:**\n",
    "\n",
    "\n",
    "**Part B:**\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## Part 2: Motion Data and Visualization (15 points)\n",
    "---\n",
    "\n",
    "In this section, you will work with synthetic motion data and implement visualization utilities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# SKELETON DEFINITION (PROVIDED - DO NOT MODIFY)\n",
    "\n",
    "JOINT_NAMES = [\n",
    "    'pelvis', 'left_hip', 'right_hip', 'spine1', 'left_knee', 'right_knee',\n",
    "    'spine2', 'left_ankle', 'right_ankle', 'spine3', 'left_foot', 'right_foot',\n",
    "    'neck', 'left_collar', 'right_collar', 'head', 'left_shoulder', 'right_shoulder',\n",
    "    'left_elbow', 'right_elbow', 'left_wrist', 'right_wrist'\n",
    "]\n",
    "\n",
    "PARENT_INDICES = [\n",
    "    -1, 0, 0, 0, 1, 2,\n",
    "    3, 4, 5, 6, 7, 8,\n",
    "    9, 9, 9, 12, 13, 14,\n",
    "    16, 17, 18, 19\n",
    "]\n",
    "\n",
    "NUM_JOINTS = len(JOINT_NAMES)\n",
    "\n",
    "SKELETON_CONNECTIONS = [\n",
    "    (0, 1), (0, 2), (0, 3),\n",
    "    (1, 4), (2, 5),\n",
    "    (4, 7), (5, 8),\n",
    "    (7, 10), (8, 11),\n",
    "    (3, 6), (6, 9),\n",
    "    (9, 12), (12, 15),\n",
    "    (9, 13), (9, 14),\n",
    "    (13, 16), (14, 17),\n",
    "    (16, 18), (17, 19),\n",
    "    (18, 20), (19, 21)\n",
    "]\n",
    "\n",
    "# T-pose reference positions\n",
    "T_POSE = np.array([\n",
    "    [0, 0, 0],       # pelvis\n",
    "    [-0.1, 0, 0],    # left_hip\n",
    "    [0.1, 0, 0],     # right_hip\n",
    "    [0, 0.1, 0],     # spine1\n",
    "    [-0.1, -0.4, 0], # left_knee\n",
    "    [0.1, -0.4, 0],  # right_knee\n",
    "    [0, 0.25, 0],    # spine2\n",
    "    [-0.1, -0.8, 0], # left_ankle\n",
    "    [0.1, -0.8, 0],  # right_ankle\n",
    "    [0, 0.4, 0],     # spine3\n",
    "    [-0.1, -0.85, 0.05], # left_foot\n",
    "    [0.1, -0.85, 0.05],  # right_foot\n",
    "    [0, 0.55, 0],    # neck\n",
    "    [-0.05, 0.5, 0], # left_collar\n",
    "    [0.05, 0.5, 0],  # right_collar\n",
    "    [0, 0.7, 0],     # head\n",
    "    [-0.2, 0.45, 0], # left_shoulder\n",
    "    [0.2, 0.45, 0],  # right_shoulder\n",
    "    [-0.35, 0.25, 0], # left_elbow\n",
    "    [0.35, 0.25, 0],  # right_elbow\n",
    "    [-0.45, 0.05, 0], # left_wrist\n",
    "    [0.45, 0.05, 0],  # right_wrist\n",
    "], dtype=np.float32)\n",
    "\n",
    "# Reference bone lengths (for post-processing)\n",
    "BONE_LENGTHS = []\n",
    "for (start, end) in SKELETON_CONNECTIONS:\n",
    "    length = np.linalg.norm(T_POSE[end] - T_POSE[start])\n",
    "    BONE_LENGTHS.append(length)\n",
    "BONE_LENGTHS = np.array(BONE_LENGTHS, dtype=np.float32)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# HELPER FUNCTIONS (PROVIDED - DO NOT MODIFY)\n",
    "# These functions handle post-processing to ensure physically plausible outputs\n",
    "\n",
    "def normalize_bone_lengths(motion: torch.Tensor, strength: float = 0.9) -> torch.Tensor:\n",
    "    \"\"\"\n",
    "    Post-process motion to fix bone length artifacts from high CFG values.\n",
    "    Iteratively adjusts joint positions to maintain correct bone lengths.\n",
    "    \n",
    "    Args:\n",
    "        motion: (batch, seq_len, num_joints, 3) tensor\n",
    "        strength: How strongly to enforce bone lengths (0-1)\n",
    "    \n",
    "    Returns:\n",
    "        Corrected motion tensor\n",
    "    \"\"\"\n",
    "    motion = motion.clone()\n",
    "    ref_lengths = torch.tensor(BONE_LENGTHS, device=motion.device, dtype=motion.dtype)\n",
    "    \n",
    "    for _ in range(3):  # 3 iterations\n",
    "        for idx, (parent, child) in enumerate(SKELETON_CONNECTIONS):\n",
    "            bone_vec = motion[:, :, child] - motion[:, :, parent]\n",
    "            current_length = torch.norm(bone_vec, dim=-1, keepdim=True) + 1e-8\n",
    "            scale = strength * (ref_lengths[idx] / current_length) + (1 - strength)\n",
    "            motion[:, :, child] = motion[:, :, parent] + bone_vec * scale\n",
    "    \n",
    "    return motion\n",
    "\n",
    "\n",
    "def compute_dynamic_cfg_scale(\n",
    "    guidance_scale: float, \n",
    "    t: torch.Tensor, \n",
    "    num_timesteps: int\n",
    ") -> torch.Tensor:\n",
    "    \"\"\"\n",
    "    Compute dynamic CFG scale that reduces at low noise levels.\n",
    "    This prevents artifacts that occur when applying strong guidance\n",
    "    to nearly-clean samples.\n",
    "    \n",
    "    At high t (lots of noise): returns full guidance_scale\n",
    "    At low t (little noise): returns reduced guidance (~30% of original)\n",
    "    \n",
    "    Args:\n",
    "        guidance_scale: Base guidance scale (e.g., 2.5 or 5.0)\n",
    "        t: (batch,) current timesteps\n",
    "        num_timesteps: Total number of diffusion steps\n",
    "    \n",
    "    Returns:\n",
    "        (batch, 1, 1, 1) dynamic scale tensor for broadcasting\n",
    "    \"\"\"\n",
    "    t_normalized = t.float() / num_timesteps\n",
    "    return guidance_scale * (0.3 + 0.7 * t_normalized.view(-1, 1, 1, 1))\n",
    "\n",
    "\n",
    "def clamp_motion(motion: torch.Tensor, max_dist: float = 1.2) -> torch.Tensor:\n",
    "    \"\"\"\n",
    "    Clamp joint positions to reasonable bounds relative to pelvis.\n",
    "    \n",
    "    Args:\n",
    "        motion: (batch, seq_len, num_joints, 3) tensor\n",
    "        max_dist: Maximum distance from pelvis\n",
    "    \n",
    "    Returns:\n",
    "        Clamped motion tensor\n",
    "    \"\"\"\n",
    "    pelvis = motion[:, :, 0:1] \n",
    "    relative = motion - pelvis\n",
    "    relative = torch.clamp(relative, -max_dist, max_dist)\n",
    "    return pelvis + relative"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 2.1: Synthetic Motion Generation (5 points)\n",
    "\n",
    "Implement a function to generate synthetic motion data representing different action types. This will serve as our training data for the simplified MDM.\n",
    "\n",
    "**Skeleton Structure Reminder:**\n",
    "- Joint 0 (pelvis): Root of the skeleton - controls overall body position\n",
    "- Joints 3,6,9,12,15: Spine chain (spine1 → spine2 → spine3 → neck → head)\n",
    "- Joints 1,4,7,10: Left leg (hip → knee → ankle → toe)\n",
    "- Joints 2,5,8,11: Right leg (hip → knee → ankle → toe)\n",
    "- Joints 13,16,18,20: Left arm (shoulder → elbow → wrist → hand)\n",
    "- Joints 14,17,19,21: Right arm (shoulder → elbow → wrist → hand)\n",
    "\n",
    "**Coordinate System:**\n",
    "- X: Left/Right (negative = left)\n",
    "- Y: Up/Down (positive = up)\n",
    "- Z: Forward/Backward (positive = forward)\n",
    "\n",
    "**Animation Pattern Example (for a single bouncing pelvis):**\n",
    "```python\n",
    "for i, ti in enumerate(t):\n",
    "    phase = 2 * np.pi * frequency * ti  # Cyclic phase\n",
    "    motion[i, 0] = [0, bounce_height * np.sin(phase), forward_speed * ti]\n",
    "```\n",
    "\n",
    "**Tips:**\n",
    "- Use `np.sin()` and `np.cos()` for cyclic motions (legs, arms)\n",
    "- Child joints should be positioned relative to parent joints\n",
    "- Opposite limbs (left/right leg) should be in opposite phase (`phase + np.pi`)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_synthetic_motion(\n",
    "    action_type: str,\n",
    "    num_frames: int = 60,\n",
    "    fps: int = 20\n",
    ") -> np.ndarray:\n",
    "    \"\"\"\n",
    "    Generate synthetic motion data for different action types.\n",
    "    \n",
    "    Args:\n",
    "        action_type: One of ['walk', 'run', 'jump', 'wave', 'sit']\n",
    "        num_frames: Number of frames in the motion sequence\n",
    "        fps: Frames per second\n",
    "        \n",
    "    Returns:\n",
    "        motion: np.ndarray of shape (num_frames, num_joints, 3)\n",
    "                representing 3D joint positions over time\n",
    "    \"\"\"\n",
    "    t = np.linspace(0, num_frames / fps, num_frames)\n",
    "    motion = np.zeros((num_frames, NUM_JOINTS, 3))\n",
    "    \n",
    "    if action_type == 'walk':\n",
    "        # ============================================================\n",
    "        # YOUR CODE HERE: Implement walking motion\n",
    "        # - Pelvis should translate forward with slight vertical bounce\n",
    "        # - Legs should swing in alternating pattern\n",
    "        # - Arms should swing opposite to legs\n",
    "        # \n",
    "        # Hints:\n",
    "        # - Use sinusoidal functions for cyclic motion\n",
    "        # - walk_freq ~ 1.5 Hz, step_length ~ 0.3, bounce ~ 0.03\n",
    "        # - Left leg phase = phase, Right leg phase = phase + pi\n",
    "        # ============================================================\n",
    "        raise NotImplementedError(\"Implement walking motion\")\n",
    "        \n",
    "    elif action_type == 'run':\n",
    "        # ============================================================\n",
    "        # YOUR CODE HERE: Implement running motion\n",
    "        # - Faster leg cycling than walk (freq ~ 2.5 Hz)\n",
    "        # - Higher vertical bounce (~ 0.08)\n",
    "        # - More pronounced arm swing\n",
    "        # - Forward lean in spine\n",
    "        # ============================================================\n",
    "        raise NotImplementedError(\"Implement running motion\")\n",
    "        \n",
    "    elif action_type == 'jump':\n",
    "        # ============================================================\n",
    "        # YOUR CODE HERE: Implement jumping motion\n",
    "        # Phases:\n",
    "        # - 0-30%: Crouch preparation (pelvis lowers, knees bend)\n",
    "        # - 30-50%: Launch (pelvis rises, arms raise)\n",
    "        # - 50-80%: Air time (peak height)\n",
    "        # - 80-100%: Landing (pelvis lowers, knees bend to absorb)\n",
    "        # ============================================================\n",
    "        raise NotImplementedError(\"Implement jumping motion\")\n",
    "        \n",
    "    elif action_type == 'wave':\n",
    "        # ============================================================\n",
    "        # YOUR CODE HERE: Implement waving motion\n",
    "        # - Body stays relatively stationary\n",
    "        # - Right arm raises (shoulder up, elbow bent)\n",
    "        # - Wrist waves side to side (freq ~ 3 Hz)\n",
    "        # - Slight body sway\n",
    "        # ============================================================\n",
    "        raise NotImplementedError(\"Implement waving motion\")\n",
    "        \n",
    "    elif action_type == 'sit':\n",
    "        # ============================================================\n",
    "        # YOUR CODE HERE: Implement sitting down motion\n",
    "        # - Pelvis lowers over time (0 to -0.4)\n",
    "        # - Pelvis moves slightly backward\n",
    "        # - Knees bend significantly (move forward)\n",
    "        # - Arms rest on thighs in final pose\n",
    "        # ============================================================\n",
    "        raise NotImplementedError(\"Implement sitting motion\")\n",
    "        \n",
    "    else:\n",
    "        raise ValueError(f\"Unknown action type: {action_type}\")\n",
    "    \n",
    "    return motion.astype(np.float32)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Test your implementation\n",
    "walk_motion = generate_synthetic_motion(\"walk\")\n",
    "print(f\"Walking motion shape: {walk_motion.shape}\")\n",
    "print(f\"Expected: (60, 22, 3)\")\n",
    "\n",
    "if walk_motion.shape == (60, 22, 3):\n",
    "    print(\"Shape correct\")\n",
    "else:\n",
    "    print(\"Shape incorrect\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 2.2: Motion Visualization as GIF (5 points)\n",
    "\n",
    "Implement a function to visualize motion sequences as animated GIFs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def visualize_motion_as_gif(\n",
    "    motion: np.ndarray,\n",
    "    filename: str = 'motion.gif',\n",
    "    fps: int = 20,\n",
    "    title: str = '',\n",
    "    elevation: int = 15,\n",
    "    azimuth: int = 45\n",
    ") -> str:\n",
    "    \"\"\"\n",
    "    Visualize a motion sequence as an animated GIF.\n",
    "    \n",
    "    Args:\n",
    "        motion: np.ndarray of shape (num_frames, num_joints, 3)\n",
    "        filename: Output GIF filename\n",
    "        fps: Frames per second for the GIF\n",
    "        title: Title for the animation\n",
    "        elevation: Camera elevation angle\n",
    "        azimuth: Camera azimuth angle\n",
    "        \n",
    "    Returns:\n",
    "        filename: Path to the saved GIF\n",
    "    \"\"\"\n",
    "    num_frames = motion.shape[0]\n",
    "    frames = []\n",
    "    \n",
    "    # ============================================================\n",
    "    # YOUR CODE HERE:\n",
    "    # 1. Calculate axis bounds from motion data\n",
    "    # 2. For each frame:\n",
    "    #    a. Create 3D figure\n",
    "    #    b. Plot joints as scatter points (use different colors for\n",
    "    #       torso/left/right: blue/green/red)\n",
    "    #    c. Plot bones as lines using SKELETON_CONNECTIONS\n",
    "    #    d. Set axis limits, labels, view angle\n",
    "    #    e. Convert figure to image array\n",
    "    # 3. Save frames as GIF using imageio.mimsave()\n",
    "    # ============================================================\n",
    "    \n",
    "    raise NotImplementedError(\"Implement motion visualization\")\n",
    "    \n",
    "    return filename"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Reference visualization implementation (PROVIDED)\n",
    "def visualize_motion_as_gif_reference(\n",
    "    motion: np.ndarray,\n",
    "    filename: str = 'motion.gif',\n",
    "    fps: int = 20,\n",
    "    title: str = '',\n",
    "    elevation: int = 15,\n",
    "    azimuth: int = 45\n",
    ") -> str:\n",
    "    \"\"\"Reference implementation for motion visualization.\"\"\"\n",
    "    num_frames = motion.shape[0]\n",
    "    frames = []\n",
    "\n",
    "    x_min, x_max = motion[:, :, 0].min() - 0.3, motion[:, :, 0].max() + 0.3\n",
    "    y_min, y_max = motion[:, :, 1].min() - 0.3, motion[:, :, 1].max() + 0.3\n",
    "    z_min, z_max = motion[:, :, 2].min() - 0.3, motion[:, :, 2].max() + 0.3\n",
    "\n",
    "    max_range = max(x_max - x_min, y_max - y_min, z_max - z_min) / 2\n",
    "    x_mid, y_mid, z_mid = (x_max + x_min) / 2, (y_max + y_min) / 2, (z_max + z_min) / 2\n",
    "\n",
    "    torso_idx = [0, 3, 6, 9, 12, 15]\n",
    "    left_idx = [1, 4, 7, 10, 13, 16, 18, 20]\n",
    "    right_idx = [2, 5, 8, 11, 14, 17, 19, 21]\n",
    "\n",
    "    for frame_idx in tqdm(range(num_frames), desc=\"Rendering\"):\n",
    "        fig = plt.figure(figsize=(8, 8))\n",
    "        ax = fig.add_subplot(111, projection='3d')\n",
    "\n",
    "        joints = motion[frame_idx]\n",
    "\n",
    "        ax.scatter(joints[torso_idx, 0], joints[torso_idx, 2], joints[torso_idx, 1], c='blue', s=60)\n",
    "        ax.scatter(joints[left_idx, 0], joints[left_idx, 2], joints[left_idx, 1], c='green', s=50)\n",
    "        ax.scatter(joints[right_idx, 0], joints[right_idx, 2], joints[right_idx, 1], c='red', s=50)\n",
    "\n",
    "        for (start, end) in SKELETON_CONNECTIONS:\n",
    "            if start in left_idx or end in left_idx:\n",
    "                color = 'green'\n",
    "            elif start in right_idx or end in right_idx:\n",
    "                color = 'red'\n",
    "            else:\n",
    "                color = 'blue'\n",
    "            ax.plot3D([joints[start, 0], joints[end, 0]],\n",
    "                      [joints[start, 2], joints[end, 2]],\n",
    "                      [joints[start, 1], joints[end, 1]],\n",
    "                      color=color, linewidth=2.5)\n",
    "\n",
    "        ax.set_xlim([x_mid - max_range, x_mid + max_range])\n",
    "        ax.set_ylim([z_mid - max_range, z_mid + max_range])\n",
    "        ax.set_zlim([y_mid - max_range, y_mid + max_range])\n",
    "        ax.view_init(elev=elevation, azim=azimuth)\n",
    "        ax.set_title(f\"{title} - Frame {frame_idx + 1}/{num_frames}\")\n",
    "\n",
    "        fig.canvas.draw()\n",
    "        image = np.asarray(fig.canvas.buffer_rgba()) \n",
    "        frames.append(image)\n",
    "        plt.close(fig)\n",
    "\n",
    "    imageio.mimsave(filename, frames, fps=fps, loop=0)\n",
    "    print(f\"Saved: {filename}\")\n",
    "    return filename\n",
    "\n",
    "visualize_motion_as_gif_reference(walk_motion, 'walk_test.gif', title='Walking')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Display the GIF\n",
    "from IPython.display import Image as IPyImage, display\n",
    "display(IPyImage(filename='walk_test.gif'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 2.3: Motion Features (5 points)\n",
    "\n",
    "Implement functions to compute motion features used in MDM's geometric losses."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_velocity(motion: torch.Tensor) -> torch.Tensor:\n",
    "    \"\"\"\n",
    "    Compute joint velocities from position sequence.\n",
    "    \n",
    "    Args:\n",
    "        motion: (batch, frames, joints, 3) tensor of joint positions\n",
    "        \n",
    "    Returns:\n",
    "        velocity: (batch, frames-1, joints, 3) tensor of velocities\n",
    "    \"\"\"\n",
    "    # ============================================================\n",
    "    # YOUR CODE HERE: Compute velocity as finite differences\n",
    "    # v[t] = x[t+1] - x[t]\n",
    "    # ============================================================\n",
    "    raise NotImplementedError()\n",
    "\n",
    "\n",
    "def compute_acceleration(motion: torch.Tensor) -> torch.Tensor:\n",
    "    \"\"\"\n",
    "    Compute joint accelerations from position sequence.\n",
    "    \n",
    "    Args:\n",
    "        motion: (batch, frames, joints, 3) tensor of joint positions\n",
    "        \n",
    "    Returns:\n",
    "        acceleration: (batch, frames-2, joints, 3) tensor of accelerations\n",
    "    \"\"\"\n",
    "    # ============================================================\n",
    "    # YOUR CODE HERE: Compute acceleration as second-order differences\n",
    "    # a[t] = x[t+1] - 2*x[t] + x[t-1]\n",
    "    # ============================================================\n",
    "    raise NotImplementedError()\n",
    "\n",
    "\n",
    "def compute_foot_contact(\n",
    "    motion: torch.Tensor,\n",
    "    left_foot_idx: int = 10,\n",
    "    right_foot_idx: int = 11,\n",
    "    height_threshold: float = 0.05,\n",
    "    velocity_threshold: float = 0.02\n",
    ") -> torch.Tensor:\n",
    "    \"\"\"\n",
    "    Compute binary foot contact labels.\n",
    "    A foot is in contact when both:\n",
    "    1. Its height (Y) is below threshold\n",
    "    2. Its velocity magnitude is below threshold\n",
    "    \n",
    "    Args:\n",
    "        motion: (batch, frames, joints, 3) tensor\n",
    "        \n",
    "    Returns:\n",
    "        contact: (batch, frames, 2) binary tensor [left, right]\n",
    "    \"\"\"\n",
    "    # ============================================================\n",
    "    # YOUR CODE HERE: Implement foot contact detection\n",
    "    # ============================================================\n",
    "    raise NotImplementedError()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## Part 3: MDM Architecture Implementation (30 points)\n",
    "---\n",
    "\n",
    "In this section, you will implement the core components of the Motion Diffusion Model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 3.1: Positional Encodings (5 points)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "class SinusoidalPositionalEncoding(nn.Module):\n",
    "    \"\"\"\n",
    "    Sinusoidal positional encoding for diffusion timesteps and sequence positions.\n",
    "    \"\"\"\n",
    "    def __init__(self, dim: int, max_len: int = 5000):\n",
    "        super().__init__()\n",
    "        self.dim = dim\n",
    "        \n",
    "        # ============================================================\n",
    "        # YOUR CODE HERE:\n",
    "        # Create positional encoding matrix of shape (max_len, dim)\n",
    "        # PE(pos, 2i) = sin(pos / 10000^(2i/dim))\n",
    "        # PE(pos, 2i+1) = cos(pos / 10000^(2i/dim))\n",
    "        # Register as buffer using self.register_buffer('pe', pe)\n",
    "        # ============================================================\n",
    "        raise NotImplementedError()\n",
    "        \n",
    "    def forward(self, positions: torch.Tensor) -> torch.Tensor:\n",
    "        \"\"\"Return positional encodings for given positions.\"\"\"\n",
    "        # ============================================================\n",
    "        # YOUR CODE HERE: Index into self.pe\n",
    "        # ============================================================\n",
    "        raise NotImplementedError()\n",
    "\n",
    "\n",
    "class TimestepEmbedding(nn.Module):\n",
    "    \"\"\"\n",
    "    Timestep embedding: sinusoidal encoding + MLP.\n",
    "    \"\"\"\n",
    "    def __init__(self, dim: int, hidden_dim: int = None):\n",
    "        super().__init__()\n",
    "        hidden_dim = hidden_dim or dim * 4\n",
    "        \n",
    "        # ============================================================\n",
    "        # YOUR CODE HERE:\n",
    "        # 1. Create SinusoidalPositionalEncoding\n",
    "        # 2. Create MLP: Linear(dim, hidden) -> SiLU -> Linear(hidden, dim)\n",
    "        # ============================================================\n",
    "        raise NotImplementedError()\n",
    "        \n",
    "    def forward(self, timesteps: torch.Tensor) -> torch.Tensor:\n",
    "        # ============================================================\n",
    "        # YOUR CODE HERE: PE -> MLP\n",
    "        # ============================================================\n",
    "        raise NotImplementedError()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 3.2: Transformer Encoder Block (10 points)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "class TransformerEncoderBlock(nn.Module):\n",
    "    \"\"\"\n",
    "    Pre-norm transformer encoder block.\n",
    "    \n",
    "    Structure:\n",
    "    x -> LayerNorm -> MultiHeadAttention -> + -> LayerNorm -> MLP -> +\n",
    "    |___________________________________|   |___________________|  \n",
    "              (residual)                        (residual)\n",
    "    \"\"\"\n",
    "    def __init__(\n",
    "        self,\n",
    "        dim: int,\n",
    "        num_heads: int = 8,\n",
    "        mlp_ratio: float = 4.0,\n",
    "        dropout: float = 0.1\n",
    "    ):\n",
    "        super().__init__()\n",
    "        \n",
    "        # ============================================================\n",
    "        # YOUR CODE HERE:\n",
    "        # 1. Two LayerNorm layers\n",
    "        # 2. MultiheadAttention (use batch_first=True)\n",
    "        # 3. MLP: Linear -> GELU -> Dropout -> Linear -> Dropout\n",
    "        # 4. Dropout for residual\n",
    "        # ============================================================\n",
    "        raise NotImplementedError()\n",
    "        \n",
    "    def forward(self, x: torch.Tensor, mask: Optional[torch.Tensor] = None) -> torch.Tensor:\n",
    "        \"\"\"\n",
    "        Args:\n",
    "            x: (batch, seq_len, dim)\n",
    "            mask: Optional attention mask\n",
    "        \"\"\"\n",
    "        # ============================================================\n",
    "        # YOUR CODE HERE: Pre-norm with residuals\n",
    "        # ============================================================\n",
    "        raise NotImplementedError()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 3.3: Motion Diffusion Model (15 points)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "class MotionDiffusionModel(nn.Module):\n",
    "    \"\"\"\n",
    "    Motion Diffusion Model (MDM) for human motion generation.\n",
    "    \n",
    "    Architecture:\n",
    "    1. Input projection: flatten joints -> hidden_dim\n",
    "    2. Add temporal positional encoding\n",
    "    3. Add timestep embedding (broadcast to all frames)\n",
    "    4. Add action embedding with classifier-free masking\n",
    "    5. Stack of transformer encoder blocks\n",
    "    6. Output projection: hidden_dim -> flatten joints\n",
    "    \"\"\"\n",
    "    def __init__(\n",
    "        self,\n",
    "        num_joints: int = 22,\n",
    "        joint_dim: int = 3,\n",
    "        hidden_dim: int = 256,\n",
    "        num_layers: int = 6,\n",
    "        num_heads: int = 4,\n",
    "        num_actions: int = 5,\n",
    "        max_seq_len: int = 196,\n",
    "        dropout: float = 0.1,\n",
    "        cond_mask_prob: float = 0.1  # Probability of masking condition for CFG\n",
    "    ):\n",
    "        super().__init__()\n",
    "        \n",
    "        self.num_joints = num_joints\n",
    "        self.joint_dim = joint_dim\n",
    "        self.motion_dim = num_joints * joint_dim\n",
    "        self.hidden_dim = hidden_dim\n",
    "        self.cond_mask_prob = cond_mask_prob\n",
    "        \n",
    "        # ============================================================\n",
    "        # YOUR CODE HERE:\n",
    "        # 1. input_proj: Linear(motion_dim, hidden_dim)\n",
    "        # 2. output_proj: LayerNorm -> Linear(hidden_dim, motion_dim)\n",
    "        # 3. timestep_emb: TimestepEmbedding\n",
    "        # 4. action_emb: Embedding(num_actions + 1, hidden_dim)\n",
    "        #    Note: +1 for null token used in classifier-free guidance\n",
    "        # 5. pos_enc: SinusoidalPositionalEncoding\n",
    "        # 6. blocks: ModuleList of TransformerEncoderBlock\n",
    "        # \n",
    "        # Store null_action_idx = num_actions for CFG\n",
    "        # ============================================================\n",
    "        raise NotImplementedError()\n",
    "        \n",
    "    def forward(\n",
    "        self,\n",
    "        x: torch.Tensor,\n",
    "        timesteps: torch.Tensor,\n",
    "        action: Optional[torch.Tensor] = None,\n",
    "        mask: Optional[torch.Tensor] = None,\n",
    "        force_mask: bool = False  \n",
    "    ) -> torch.Tensor:\n",
    "        \"\"\"\n",
    "        Args:\n",
    "            x: (batch, seq_len, num_joints, joint_dim) noisy motion\n",
    "            timesteps: (batch,) diffusion timesteps\n",
    "            action: (batch,) action class indices\n",
    "            mask: Optional sequence mask\n",
    "            force_mask: If True, use null embedding (for CFG)\n",
    "            \n",
    "        Returns:\n",
    "            x0_pred: (batch, seq_len, num_joints, joint_dim) predicted clean motion\n",
    "        \"\"\"\n",
    "        batch_size, seq_len = x.shape[:2]\n",
    "        \n",
    "        x = x.view(batch_size, seq_len, -1)\n",
    "        \n",
    "        # ============================================================\n",
    "        # YOUR CODE HERE:\n",
    "        # 1. Project input: h = input_proj(x)\n",
    "        # 2. Add positional encoding (for seq positions 0 to seq_len-1)\n",
    "        # 3. Add timestep embedding (unsqueeze to broadcast)\n",
    "        # 4. Handle action embedding with classifier-free masking:\n",
    "        #    - If force_mask: always use null embedding\n",
    "        #    - If training: randomly replace action with null (prob=cond_mask_prob)\n",
    "        #    - Add action embedding (unsqueeze to broadcast)\n",
    "        # 5. Pass through transformer blocks\n",
    "        # 6. Output projection and reshape to (batch, seq, joints, 3)\n",
    "        # ============================================================\n",
    "        raise NotImplementedError()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## Part 4: Diffusion Training and Sampling (20 points)\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 4.1: Gaussian Diffusion Process (5 points)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "class GaussianDiffusion:\n",
    "    \"\"\"\n",
    "    Gaussian diffusion process with cosine noise schedule.\n",
    "    \"\"\"\n",
    "    def __init__(\n",
    "        self,\n",
    "        num_timesteps: int = 1000,\n",
    "        schedule: str = 'cosine',\n",
    "        s: float = 0.008  \n",
    "    ):\n",
    "        self.num_timesteps = num_timesteps\n",
    "        \n",
    "        # ============================================================\n",
    "        # YOUR CODE HERE:\n",
    "        # 1. Implement cosine schedule:\n",
    "        #    f(t) = cos((t/T + s)/(1 + s) * pi/2)^2\n",
    "        #    alpha_bar_t = f(t) / f(0)\n",
    "        #    beta_t = 1 - alpha_bar_t / alpha_bar_{t-1}\n",
    "        #    Clip betas to [0.0001, 0.9999]\n",
    "        #\n",
    "        # 2. Compute and store as torch tensors:\n",
    "        #    - betas, alphas, alphas_cumprod, alphas_cumprod_prev\n",
    "        #    - sqrt_alphas_cumprod, sqrt_one_minus_alphas_cumprod\n",
    "        #    - posterior_variance, posterior_log_variance_clipped\n",
    "        #    - posterior_mean_coef1, posterior_mean_coef2\n",
    "        # ============================================================\n",
    "        raise NotImplementedError()\n",
    "    \n",
    "    def _extract(self, arr: torch.Tensor, t: torch.Tensor, shape: tuple) -> torch.Tensor:\n",
    "        \"\"\"Extract values at timestep t and reshape for broadcasting.\"\"\"\n",
    "        arr = arr.to(t.device)\n",
    "        return arr[t].view([t.shape[0]] + [1] * (len(shape) - 1))\n",
    "        \n",
    "    def q_sample(\n",
    "        self,\n",
    "        x_0: torch.Tensor,\n",
    "        t: torch.Tensor,\n",
    "        noise: Optional[torch.Tensor] = None\n",
    "    ) -> Tuple[torch.Tensor, torch.Tensor]:\n",
    "        \"\"\"\n",
    "        Forward diffusion: q(x_t | x_0) = N(sqrt(alpha_bar)*x_0, (1-alpha_bar)*I)\n",
    "        \n",
    "        Returns: (x_t, noise)\n",
    "        \"\"\"\n",
    "        # ============================================================\n",
    "        # YOUR CODE HERE\n",
    "        # ============================================================\n",
    "        raise NotImplementedError()\n",
    "    \n",
    "    def q_posterior(\n",
    "        self,\n",
    "        x_0: torch.Tensor,\n",
    "        x_t: torch.Tensor,\n",
    "        t: torch.Tensor\n",
    "    ) -> Tuple[torch.Tensor, torch.Tensor]:\n",
    "        \"\"\"\n",
    "        Compute posterior q(x_{t-1} | x_t, x_0).\n",
    "        \n",
    "        Returns: (posterior_mean, posterior_log_variance)\n",
    "        \"\"\"\n",
    "        # ============================================================\n",
    "        # YOUR CODE HERE\n",
    "        # ============================================================\n",
    "        raise NotImplementedError()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 4.2: Geometric Losses (5 points)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "class MotionLosses:\n",
    "    \"\"\"\n",
    "    Geometric losses for motion generation.\n",
    "    \"\"\"\n",
    "    \n",
    "    @staticmethod\n",
    "    def reconstruction_loss(\n",
    "        pred: torch.Tensor,\n",
    "        target: torch.Tensor,\n",
    "        mask: Optional[torch.Tensor] = None\n",
    "    ) -> torch.Tensor:\n",
    "        \"\"\"\n",
    "        L2 loss on joint positions.\n",
    "        \"\"\"\n",
    "        # ============================================================\n",
    "        # YOUR CODE HERE: MSE loss, handle optional mask\n",
    "        # ============================================================\n",
    "        raise NotImplementedError()\n",
    "    \n",
    "    @staticmethod\n",
    "    def velocity_loss(\n",
    "        pred: torch.Tensor,\n",
    "        target: torch.Tensor,\n",
    "        mask: Optional[torch.Tensor] = None\n",
    "    ) -> torch.Tensor:\n",
    "        \"\"\"\n",
    "        L2 loss on joint velocities for smooth motion.\n",
    "        \"\"\"\n",
    "        # ============================================================\n",
    "        # YOUR CODE HERE: Compute velocities, then MSE\n",
    "        # ============================================================\n",
    "        raise NotImplementedError()\n",
    "    \n",
    "    @staticmethod\n",
    "    def foot_contact_loss(\n",
    "        pred: torch.Tensor,\n",
    "        target_contacts: torch.Tensor,\n",
    "        left_foot_idx: int = 10,\n",
    "        right_foot_idx: int = 11\n",
    "    ) -> torch.Tensor:\n",
    "        \"\"\"\n",
    "        Foot skating loss: when contact=1, foot velocity should be 0.\n",
    "        \"\"\"\n",
    "        # ============================================================\n",
    "        # YOUR CODE HERE: \n",
    "        # 1. Get foot velocities\n",
    "        # 2. Penalize velocity when contact label is 1\n",
    "        # ============================================================\n",
    "        raise NotImplementedError()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 4.3: DDPM Sampling with Classifier-Free Guidance (10 points)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "class MDMSampler:\n",
    "    \"\"\"\n",
    "    DDPM sampler with classifier-free guidance for MDM.\n",
    "    \n",
    "    IMPORTANT: Use the provided helper functions to ensure correct outputs:\n",
    "    - compute_dynamic_cfg_scale(): Reduces CFG at low noise levels\n",
    "    - normalize_bone_lengths(): Fixes bone stretching artifacts\n",
    "    - clamp_motion(): Keeps joints in reasonable bounds\n",
    "    \"\"\"\n",
    "    def __init__(\n",
    "        self,\n",
    "        model: nn.Module,\n",
    "        diffusion: GaussianDiffusion,\n",
    "        device: torch.device = device\n",
    "    ):\n",
    "        self.model = model\n",
    "        self.diffusion = diffusion\n",
    "        self.device = device\n",
    "        \n",
    "    @torch.no_grad()\n",
    "    def p_sample(\n",
    "        self,\n",
    "        x: torch.Tensor,\n",
    "        t: torch.Tensor,\n",
    "        action: Optional[torch.Tensor] = None,\n",
    "        guidance_scale: float = 1.0\n",
    "    ) -> torch.Tensor:\n",
    "        \"\"\"\n",
    "        Single reverse diffusion step with classifier-free guidance.\n",
    "        \n",
    "        Args:\n",
    "            x: (batch, seq_len, joints, 3) current noisy sample\n",
    "            t: (batch,) current timestep\n",
    "            action: (batch,) action class\n",
    "            guidance_scale: CFG scale (w >= 1.0)\n",
    "        \"\"\"\n",
    "        # ============================================================\n",
    "        # YOUR CODE HERE:\n",
    "        # 1. Get conditional prediction: x0_pred = model(x, t, action)\n",
    "        #\n",
    "        # 2. If guidance_scale > 1.0, apply classifier-free guidance:\n",
    "        #    a. Get unconditional prediction: model(x, t, action, force_mask=True)\n",
    "        #    b. Use DYNAMIC CFG scale (important for preventing artifacts!):\n",
    "        #       dynamic_scale = compute_dynamic_cfg_scale(guidance_scale, t, self.diffusion.num_timesteps)\n",
    "        #    c. Combine: x0_pred = x0_pred + dynamic_scale * (x0_pred - x0_pred_uncond)\n",
    "        #\n",
    "        # 3. Clamp prediction: x0_pred = clamp_motion(x0_pred)\n",
    "        #\n",
    "        # 4. Compute posterior: mean, log_var = diffusion.q_posterior(x0_pred, x, t)\n",
    "        #\n",
    "        # 5. Sample x_{t-1}:\n",
    "        #    - If t > 0: add noise scaled by exp(0.5 * log_var)\n",
    "        #    - If t = 0: no noise (final sample)\n",
    "        # ============================================================\n",
    "        raise NotImplementedError()\n",
    "        \n",
    "    @torch.no_grad()\n",
    "    def sample(\n",
    "        self,\n",
    "        batch_size: int,\n",
    "        seq_len: int,\n",
    "        action: Optional[torch.Tensor] = None,\n",
    "        guidance_scale: float = 2.5,\n",
    "        show_progress: bool = True\n",
    "    ) -> torch.Tensor:\n",
    "        \"\"\"\n",
    "        Full DDPM sampling loop.\n",
    "        \"\"\"\n",
    "        self.model.eval()\n",
    "        \n",
    "        # ============================================================\n",
    "        # YOUR CODE HERE:\n",
    "        # 1. Start from pure noise: x ~ N(0, I)\n",
    "        # 2. Loop from t = T-1 down to 0:\n",
    "        #    x = self.p_sample(x, t, action, guidance_scale)\n",
    "        # 3. Post-process: x = normalize_bone_lengths(x, strength=0.9)\n",
    "        # 4. Final clamp: x = clamp_motion(x)\n",
    "        # ============================================================\n",
    "        raise NotImplementedError()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## Part 5: Training and Experiments (15 points)\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 5.1: Create Dataset (5 points)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "class SyntheticMotionDataset(torch.utils.data.Dataset):\n",
    "    \"\"\"Dataset of synthetic motion sequences.\"\"\"\n",
    "    \n",
    "    def __init__(self, num_samples: int = 500, seq_len: int = 60):\n",
    "        self.num_samples = num_samples\n",
    "        self.seq_len = seq_len\n",
    "        self.action_names = ['walk', 'run', 'jump', 'wave', 'sit']\n",
    "        \n",
    "        self.motions = []\n",
    "        self.actions = []\n",
    "        self.foot_contacts = []\n",
    "        \n",
    "        # ============================================================\n",
    "        # YOUR CODE HERE:\n",
    "        # For each sample:\n",
    "        # 1. Pick action (cycle through actions)\n",
    "        # 2. Generate motion using generate_synthetic_motion()\n",
    "        #    (or use reference implementation)\n",
    "        # 3. Add small noise for variety: motion += randn * 0.005\n",
    "        # 4. Compute foot contacts\n",
    "        # 5. Store motion, action index, contacts\n",
    "        # ============================================================\n",
    "        raise NotImplementedError()\n",
    "    \n",
    "    def __len__(self):\n",
    "        return self.num_samples\n",
    "    \n",
    "    def __getitem__(self, idx):\n",
    "        return {\n",
    "            'motion': torch.tensor(self.motions[idx]),\n",
    "            'action': torch.tensor(self.actions[idx]),\n",
    "            'foot_contact': torch.tensor(self.foot_contacts[idx])\n",
    "        }"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 5.2: Training Loop (5 points)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def train_mdm(\n",
    "    model: nn.Module,\n",
    "    diffusion: GaussianDiffusion,\n",
    "    dataloader: torch.utils.data.DataLoader,\n",
    "    num_epochs: int = 100,\n",
    "    lr: float = 1e-4,\n",
    "    lambda_vel: float = 0.5,\n",
    "    lambda_fc: float = 0.1,\n",
    "    device: torch.device = device\n",
    ") -> List[float]:\n",
    "    \"\"\"\n",
    "    Train the Motion Diffusion Model.\n",
    "    \n",
    "    Returns:\n",
    "        losses: List of epoch losses\n",
    "    \"\"\"\n",
    "    model.train()\n",
    "    optimizer = torch.optim.AdamW(model.parameters(), lr=lr, weight_decay=0.01)\n",
    "    scheduler = torch.optim.lr_scheduler.CosineAnnealingLR(optimizer, num_epochs)\n",
    "    \n",
    "    losses = []\n",
    "    best_loss = float('inf')\n",
    "    \n",
    "    for epoch in range(num_epochs):\n",
    "        epoch_loss = 0.0\n",
    "        \n",
    "        for batch in dataloader:\n",
    "            motion = batch['motion'].to(device)\n",
    "            action = batch['action'].to(device)\n",
    "            foot_contact = batch['foot_contact'].to(device)\n",
    "            batch_size = motion.shape[0]\n",
    "            \n",
    "            # ============================================================\n",
    "            # YOUR CODE HERE:\n",
    "            # 1. Sample random timesteps t ~ Uniform(0, T)\n",
    "            # 2. Add noise: noisy_motion, _ = diffusion.q_sample(motion, t)\n",
    "            # 3. Predict clean motion: x0_pred = model(noisy_motion, t, action)\n",
    "            # 4. Compute losses:\n",
    "            #    - recon_loss = reconstruction_loss(x0_pred, motion)\n",
    "            #    - vel_loss = velocity_loss(x0_pred, motion)\n",
    "            #    - fc_loss = foot_contact_loss(x0_pred, foot_contact)\n",
    "            # 5. Total: loss = recon + lambda_vel*vel + lambda_fc*fc\n",
    "            # 6. Backprop with gradient clipping (max_norm=1.0)\n",
    "            # ============================================================\n",
    "            raise NotImplementedError()\n",
    "        \n",
    "        scheduler.step()\n",
    "        epoch_loss /= len(dataloader)\n",
    "        losses.append(epoch_loss)\n",
    "        \n",
    "        if epoch_loss < best_loss:\n",
    "            best_loss = epoch_loss\n",
    "            torch.save(model.state_dict(), 'best_mdm.pt')\n",
    "        \n",
    "        if (epoch + 1) % 10 == 0:\n",
    "            print(f\"Epoch {epoch + 1}/{num_epochs} | Loss: {epoch_loss:.4f}\")\n",
    "    \n",
    "    return losses"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 5.3: Generate and Visualize Samples (5 points)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# ============================================================\n",
    "# YOUR CODE HERE:\n",
    "# 1. Create dataset and dataloader\n",
    "# 2. Initialize model and diffusion\n",
    "# 3. Train the model\n",
    "# 4. Plot training curve\n",
    "# 5. Load best model\n",
    "# 6. Generate samples for each action at CFG = [1.0, 2.5, 5.0]\n",
    "# 7. Visualize as GIFs\n",
    "# ============================================================"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## Part 6: Motion Inpainting (Bonus: 10 points)\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "class MotionInpainter:\n",
    "    \"\"\"\n",
    "    Motion inpainting: given first and last 25% of frames, generate middle 50%.\n",
    "    \"\"\"\n",
    "    def __init__(self, model, diffusion, device=device):\n",
    "        self.model = model\n",
    "        self.diffusion = diffusion\n",
    "        self.device = device\n",
    "        \n",
    "    @torch.no_grad()\n",
    "    def inpaint(\n",
    "        self,\n",
    "        motion: torch.Tensor,\n",
    "        mask: torch.Tensor,\n",
    "        action: Optional[torch.Tensor] = None,\n",
    "        guidance_scale: float = 2.5\n",
    "    ) -> torch.Tensor:\n",
    "        \"\"\"\n",
    "        Inpaint missing frames.\n",
    "        \n",
    "        Args:\n",
    "            motion: (batch, seq_len, joints, 3) partial motion\n",
    "            mask: (batch, seq_len) binary mask (1=known, 0=generate)\n",
    "            action: (batch,) action classes\n",
    "            guidance_scale: CFG scale\n",
    "        \"\"\"\n",
    "        # ============================================================\n",
    "        # YOUR CODE HERE:\n",
    "        # At each timestep t from T-1 to 0:\n",
    "        # 1. Denoise normally to get x_prev\n",
    "        # 2. For known frames (mask=1), replace with noisy ground truth:\n",
    "        #    - If t > 0: noisy_gt = q_sample(motion, t)\n",
    "        #    - If t = 0: noisy_gt = motion\n",
    "        # 3. Combine: x = mask * noisy_gt + (1-mask) * x_prev\n",
    "        # 4. Post-process with normalize_bone_lengths()\n",
    "        # ============================================================\n",
    "        raise NotImplementedError()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## Part 7: Analysis Questions (5 points)\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 7.1: Guidance Scale Analysis\n",
    "\n",
    "Based on your generated samples with different guidance scales (1.0, 2.5, 5.0):\n",
    "\n",
    "1. How does visual quality change with increasing guidance scale?\n",
    "2. What happens to sample diversity at high guidance scales?\n",
    "\n",
    "*Your answer:*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Question 7.2: Architectural Choices\n",
    "\n",
    "1. Why is transformer architecture suitable for motion (vs U-Net for images)?\n",
    "2. How does predicting x₀ (instead of noise ε) enable geometric losses?\n",
    "\n",
    "*Your answer:*"
   ]
  }
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