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Total steps: 7

Messages: 34

UserStep 0

Task: cv-diffusion-prediction

Diffusion Prediction Parameterization

Background

In DDPM training, the model predicts a target from noisy input x_t. The noisy sample is constructed as:

x_t = sqrt(alpha_t) * x_0 + sqrt(1 - alpha_t) * epsilon

There are three standard parameterizations for what the model predicts:

Epsilon prediction (Ho et al., 2020): predict the noise epsilon
X0 prediction: directly predict the clean image x_0
V-prediction (Salimans & Ho, 2022): predict the velocity v = sqrt(alpha_t) * epsilon - sqrt(1 - alpha_t) * x_0

These are mathematically equivalent (one can be converted to any other), but they result in different loss landscapes and training dynamics, leading to different FID scores under the same training budget.

Research Question

Can we design a prediction parameterization that achieves better FID than the standard epsilon, v-prediction, and x0-prediction baselines?

Task

You are given custom_train.py, a self-contained training script that trains an unconditional UNet2DModel (google/ddpm-cifar10-32 architecture) on CIFAR-10.

The editable region contains two functions:

compute_training_target(x_0, noise, timesteps, schedule) — defines what the model should predict during training.
predict_x0(model_output, x_t, timesteps, schedule) — recovers the predicted clean image from the model's output (used during DDIM sampling).

These two functions must be consistent: the sampling procedure must correctly invert the training parameterization.

The schedule dict provides precomputed noise schedule tensors:

alphas_cumprod: cumulative product of (1 - beta)
sqrt_alpha: sqrt(alphas_cumprod)
sqrt_one_minus_alpha: sqrt(1 - alphas_cumprod)

Evaluation

Dataset: CIFAR-10 (32x32)
Model: UNet2DModel (diffusers backbone) at three scales:
- Small: block_out_channels=(64,128,128,128), ~9M params, batch 128
- Medium: block_out_channels=(128,256,256,256), ~36M params, batch 128
- Large: block_out_channels=(256,512,512,512), ~140M params, batch 64
Training: 35000 steps per scale, AdamW lr=2e-4, EMA rate 0.9995, 8-GPU DDP
Inference: 50-step DDIM sampler
Metric: FID (lower is better), computed with clean-fid against CIFAR-10 train set (50k samples)

diffusers-main/custom_train.py [EDITABLE — lines 83–118 only]

     1: """Unconditional DDPM Training on CIFAR-10 with configurable prediction target.
     2: 
     3: Uses diffusers UNet2DModel (google/ddpm-cifar10-32 architecture).
     4: Only the prediction parameterization (training target + x0 recovery) is editable.
     5: """
     6: 
     7: import copy
     8: import math
     9: import os
    10: import sys
    11: import time
    12: from datetime import timedelta
    13: 
    14: import numpy as np
    15: import torch
    16: import torch.distributed as dist
    17: import torch.nn.functional as F
    18: from PIL import Image
    19: from torch.nn.parallel import DistributedDat

AssistantStep 1edit

Tool Input

1{
2  "op": "replace",
3  "filename": "diffusers-main/custom_train.py",
4  "start_line": 83,
5  "end_line": 118,
6  "content": "def compute_training_target(x_0, noise, timesteps, schedule):\n    \"\"\"Compute normalized v-prediction target with unit variance across timesteps.\n    \n    Target = (sqrt(alpha) * noise - sqrt(1-alpha) * x_0) / sqrt(alpha + (1-alpha)*sigma_x2)\n    where sigma_x2 = variance of x_0 (estimated as 0.25 for CIFAR-10 normalized to [-1,1]).\n    This ensures the target has approximately unit variance independent of timestep.\n    \"\"\"\n    sqrt_alpha = schedule[\"sqrt_alpha\"][timesteps].view(-1, 1, 1, 1)\n    sqrt_one_minus_alpha = schedule[\"sqrt_one_minus_alpha\"][timesteps].view(-1, 1, 1, 1)\n    # Variance of x_0 (estimated from CIFAR-10 normalized to [-1,1])\n    sigma_x2 = 0.25\n    # Denominator: sqrt(alpha + (1-alpha)*sigma_x2)\n    alpha = schedule[\"alphas_cumprod\"][timesteps].view(-1, 1, 1, 1)\n    denom = torch.sqrt(alpha + (1 - alpha) * sigma_x2 + 1e-8)\n    target = (sqrt_alpha * noise - sqrt_one_minus_alpha * x_0) / denom\n    return target\n\n\ndef predict_x0(model_output, x_t, timesteps, schedule):\n    \"\"\"Recover predicted x_0 from normalized v-prediction.\n    \n    Inverse of compute_training_target:\n    x_0 = sqrt(alpha) * x_t - sqrt(1-alpha) * sqrt(alpha + (1-alpha)*sigma_x2) * model_output\n    \"\"\"\n    sqrt_alpha = schedule[\"sqrt_alpha\"][timesteps].view(-1, 1, 1, 1)\n    sqrt_one_minus_alpha = schedule[\"sqrt_one_minus_alpha\"][timesteps].view(-1, 1, 1, 1)\n    sigma_x2 = 0.25\n    alpha = schedule[\"alphas_cumprod\"][timesteps].view(-1, 1, 1, 1)\n    denom = torch.sqrt(alpha + (1 - alpha) * sigma_x2 + 1e-8)\n    pred_x0 = sqrt_alpha * x_t - sqrt_one_minus_alpha * denom * model_output\n    return pred_x0"
7}

Tool ResultStep 1

OK: Replaced lines 83..118 with 31 line(s) in diffusers-main/custom_train.py. Editable range: 83–113.

[Current file: diffusers-main/custom_train.py | editable: 83–113 | total: 487 lines]
    80| # ============================================================================
    81| # Prediction parameterization (EDITABLE REGION)
    82| # ============================================================================
    83  def compute_training_target(x_0, noise, timesteps, schedule):
    84      """Compute normalized v-prediction target with unit variance across timesteps.
    85      
    86      Target = (sqrt(alpha) * noise - sqrt(1-alpha) * x_0) / sqrt(alpha + (1-alpha)*sigma_x2)
    87      where sigma_x2 = variance of x_0 (estimated as 0.25 for CIFAR-10 normalized to [-1,1]).
    88      This ensures the target has approximately unit variance independent of timestep.
    89      """
    90      sqrt_alpha = schedule["sqrt_alpha"][timesteps].view(-1, 1, 1, 1)
    91      sqrt_one_m

AssistantStep 2edit

Tool Input

1{
2  "op": "replace",
3  "filename": "diffusers-main/custom_train.py",
4  "start_line": 114,
5  "end_line": 114,
6  "content": ""
7}

Tool ResultStep 2

ERROR: Lines 114..114 exceed the editable range. You may only edit lines 83–113.

[Current file: diffusers-main/custom_train.py | editable: 83–113 | total: 487 lines]
    80| # ============================================================================
    81| # Prediction parameterization (EDITABLE REGION)
    82| # ============================================================================
    83  def compute_training_target(x_0, noise, timesteps, schedule):
    84      """Compute normalized v-prediction target with unit variance across timesteps.
    85      
    86      Target = (sqrt(alpha) * noise - sqrt(1-alpha) * x_0) / sqrt(alpha + (1-alpha)*sigma_x2)
    87      where sigma_x2 = variance of x_0 (estimated as 0.25 for CIFAR-10 normalized to [-1,1]).
    88      This ensures the target has approximately unit variance independent of timestep.
    89      """
    90      sqrt_alpha = schedule["sqrt_alpha"][timesteps].view(-1, 1, 1, 1)
    91      sqrt_one_minus_alpha = schedule

AssistantStep 3test

Tool ResultStep 3

[Test #1] (2 tests remaining; call submit(n=1) to submit this result)

### train_small (scripts/train_small.sh)
Training results:
Model parameters: 9.0M | GPUs: 8
step 200/35000 | loss 0.5056 | 17.2s
step 400/35000 | loss 0.5697 | 16.4s
step 600/35000 | loss 0.4915 | 16.5s
step 800/35000 | loss 0.4824 | 16.2s
step 1000/35000 | loss 0.4088 | 16.2s
step 1200/35000 | loss 0.4589 | 16.2s
step 1400/35000 | loss 0.4900 | 16.5s
step 1600/35000 | loss 0.5504 | 16.2s
step 1800/35000 | loss 0.4537 | 16.6s
step 2000/35000 | loss 0.4131 | 16.4s
step 2200/35000 | loss 0.4448 | 16.4s
step 2400/35000 | loss 0.5198 | 16.2s
step 2600/35000 | loss 0.4392 | 16.5s
step 2800/35000 | loss 0.4639 | 16.4s
step 3000/35000 | loss 0.4449 | 16.4s
step 3200/35000 | loss 0.4786 | 16.2s
step 3400/35000 | loss 0.4998 | 16.1s
step 3600/35000 | loss 0.4835 | 16.5s
step 3800/35000 | loss 0.4666 | 16.2s
step 4000/35000 | loss 0.4961 | 16.4s
step 4200/35000 | loss 0.4711 | 16.4s
step 4400/35000 | loss 0.5233 | 16.7s
step

AssistantStep 4edit

Tool Input

1{
2  "op": "replace",
3  "filename": "diffusers-main/custom_train.py",
4  "start_line": 83,
5  "end_line": 113,
6  "content": "def compute_training_target(x_0, noise, timesteps, schedule):\n    \"\"\"Score prediction: predict epsilon / sqrt(1-alpha).\n    \n    This target amplifies the noise at high noise levels (small alpha),\n    emphasizing learning in early diffusion steps.\n    \"\"\"\n    sqrt_one_minus_alpha = schedule[\"sqrt_one_minus_alpha\"][timesteps].view(-1, 1, 1, 1)\n    # Avoid division by zero\n    denom = sqrt_one_minus_alpha.clamp(min=1e-4)\n    target = noise / denom\n    return target\n\n\ndef predict_x0(model_output, x_t, timesteps, schedule):\n    \"\"\"Recover x_0 from score prediction.\n    \n    Given model_output = epsilon / sqrt(1-alpha),\n    we have epsilon = model_output * sqrt_one_minus_alpha.\n    Then x_0 = (x_t - sqrt_one_minus_alpha * epsilon) / sqrt(alpha)\n            = (x_t - (1-alpha) * model_output) / sqrt(alpha)\n    \"\"\"\n    sqrt_alpha = schedule[\"sqrt_alpha\"][timesteps].view(-1, 1, 1, 1)\n    sqrt_one_minus_alpha = schedule[\"sqrt_one_minus_alpha\"][timesteps].view(-1, 1, 1, 1)\n    # Compute (1-alpha) = sqrt_one_minus_alpha^2\n    one_minus_alpha = sqrt_one_minus_alpha ** 2\n    pred_x0 = (x_t - one_minus_alpha * model_output) / sqrt_alpha.clamp(min=1e-8)\n    return pred_x0"
7}

Tool ResultStep 4

OK: Replaced lines 83..113 with 27 line(s) in diffusers-main/custom_train.py. Editable range: 83–109.

[Current file: diffusers-main/custom_train.py | editable: 83–109 | total: 483 lines]
    80| # ============================================================================
    81| # Prediction parameterization (EDITABLE REGION)
    82| # ============================================================================
    83  def compute_training_target(x_0, noise, timesteps, schedule):
    84      """Score prediction: predict epsilon / sqrt(1-alpha).
    85      
    86      This target amplifies the noise at high noise levels (small alpha),
    87      emphasizing learning in early diffusion steps.
    88      """
    89      sqrt_one_minus_alpha = schedule["sqrt_one_minus_alpha"][timesteps].view(-1, 1, 1, 1)
    90      # Avoid division by zero
    91      denom = sqrt_one_minus_alpha.clamp(min=1e-4)
    92      target = noise / denom
    93      return target
    94  
    95  
    96

AssistantStep 5test

Tool ResultStep 5

[Test #2] (1 test remaining; call submit(n=2) to submit this result)

### train_small (scripts/train_small.sh)
Training results:
Model parameters: 9.0M | GPUs: 8
step 200/35000 | loss 1.1264 | 17.1s
step 400/35000 | loss 3.9692 | 16.3s
step 600/35000 | loss 32.7717 | 16.7s
step 800/35000 | loss 1.3466 | 16.1s
step 1000/35000 | loss 2.8519 | 16.1s
step 1200/35000 | loss 5.3287 | 16.4s
step 1400/35000 | loss 6.0700 | 16.7s
step 1600/35000 | loss 4.1971 | 16.3s
step 1800/35000 | loss 3.0981 | 16.5s
step 2000/35000 | loss 33.1923 | 16.1s
step 2200/35000 | loss 37.6316 | 16.2s
step 2400/35000 | loss 7.5083 | 16.1s
step 2600/35000 | loss 31.0953 | 16.4s
step 2800/35000 | loss 0.9344 | 16.3s
step 3000/35000 | loss 62.1059 | 16.8s
step 3200/35000 | loss 4.9542 | 16.2s
step 3400/35000 | loss 7.8856 | 16.1s
step 3600/35000 | loss 2.4277 | 16.3s
step 3800/35000 | loss 16.5612 | 16.6s
step 4000/35000 | loss 3.7723 | 16.1s
step 4200/35000 | loss 3.2776 | 16.1s
step 4400/35000 | loss 0.5875 | 15.9s

AssistantStep 6edit

Tool Input

1{
2  "op": "replace",
3  "filename": "diffusers-main/custom_train.py",
4  "start_line": 83,
5  "end_line": 109,
6  "content": "def compute_training_target(x_0, noise, timesteps, schedule):\n    \"\"\"Epsilon prediction: model learns to predict the added noise.\"\"\"\n    return noise\n\n\ndef predict_x0(model_output, x_t, timesteps, schedule):\n    \"\"\"Recover x_0 from epsilon prediction:\n    x_t = sqrt(alpha) * x_0 + sqrt(1-alpha) * eps\n    => x_0 = (x_t - sqrt(1-alpha) * eps) / sqrt(alpha)\n    \"\"\"\n    sqrt_alpha = schedule[\"sqrt_alpha\"][timesteps].view(-1, 1, 1, 1)\n    sqrt_one_minus_alpha = schedule[\"sqrt_one_minus_alpha\"][timesteps].view(-1, 1, 1, 1)\n    return (x_t - sqrt_one_minus_alpha * model_output) / sqrt_alpha.clamp(min=1e-8)"
7}

Tool ResultStep 6

OK: Replaced lines 83..109 with 13 line(s) in diffusers-main/custom_train.py. Editable range: 83–95.

[Current file: diffusers-main/custom_train.py | editable: 83–95 | total: 469 lines]
    80| # ============================================================================
    81| # Prediction parameterization (EDITABLE REGION)
    82| # ============================================================================
    83  def compute_training_target(x_0, noise, timesteps, schedule):
    84      """Epsilon prediction: model learns to predict the added noise."""
    85      return noise
    86  
    87  
    88  def predict_x0(model_output, x_t, timesteps, schedule):
    89      """Recover x_0 from epsilon prediction:
    90      x_t = sqrt(alpha) * x_0 + sqrt(1-alpha) * eps
    91      => x_0 = (x_t - sqrt(1-alpha) * eps) / sqrt(alpha)
    92      """
    93      sqrt_alpha = schedule["sqrt_alpha"][timesteps].view(-1, 1, 1, 1)
    94      sqrt_one_minus_alpha = schedule["sqrt_one_minus_al

AssistantStep 7test

Tool ResultStep 7

[Test #3] (0 tests remaining)

### train_small (scripts/train_small.sh)
Training results:
Model parameters: 9.0M | GPUs: 8
step 200/35000 | loss 0.0349 | 17.4s
step 400/35000 | loss 0.0323 | 16.4s
step 600/35000 | loss 0.0382 | 16.2s
step 800/35000 | loss 0.0272 | 16.2s
step 1000/35000 | loss 0.0404 | 16.1s
step 1200/35000 | loss 0.0335 | 16.2s
step 1400/35000 | loss 0.0318 | 16.4s
step 1600/35000 | loss 0.0227 | 16.2s
step 1800/35000 | loss 0.0319 | 16.2s
step 2000/35000 | loss 0.0435 | 16.4s
step 2200/35000 | loss 0.0429 | 16.0s
step 2400/35000 | loss 0.0277 | 16.1s
step 2600/35000 | loss 0.0476 | 16.3s
step 2800/35000 | loss 0.0282 | 16.2s
step 3000/35000 | loss 0.0348 | 16.0s
step 3200/35000 | loss 0.0351 | 15.8s
step 3400/35000 | loss 0.0327 | 16.1s
step 3600/35000 | loss 0.0301 | 16.2s
step 3800/35000 | loss 0.0356 | 16.4s
step 4000/35000 | loss 0.0232 | 16.2s
step 4200/35000 | loss 0.0352 | 16.2s
step 4400/35000 | loss 0.0207 | 16.1s
step 4600/35000 | loss 0.0356 | 16.2s
step 48

AssistantStep 1edit

Tool Input

1{
2  "op": "replace",
3  "filename": "diffusers-main/custom_train.py",
4  "start_line": 83,
5  "end_line": 118,
6  "content": "def compute_training_target(x_0, noise, timesteps, schedule):\n    \"\"\"Compute the training target: epsilon + lambda * sigma * x_0.\n    \n    Adds a small amount of x_0 signal to the standard epsilon prediction,\n    which may help the model learn cleaner x_0 estimates while retaining\n    the stable training dynamics of epsilon prediction.\n    \"\"\"\n    sqrt_alpha = schedule[\"sqrt_alpha\"][timesteps].view(-1, 1, 1, 1)\n    sqrt_one_minus_alpha = schedule[\"sqrt_one_minus_alpha\"][timesteps].view(-1, 1, 1, 1)\n    # Hyperparameter lambda: weight of x_0 correction term\n    lambda_val = 0.1\n    # target = epsilon + lambda * sigma * x_0\n    target = noise + lambda_val * sqrt_one_minus_alpha * x_0\n    return target\n\n\ndef predict_x0(model_output, x_t, timesteps, schedule):\n    \"\"\"Recover predicted x_0 from model output.\n    \n    Inverse of compute_training_target with same lambda.\n    \"\"\"\n    sqrt_alpha = schedule[\"sqrt_alpha\"][timesteps].view(-1, 1, 1, 1)\n    sqrt_one_minus_alpha = schedule[\"sqrt_one_minus_alpha\"][timesteps].view(-1, 1, 1, 1)\n    lambda_val = 0.1\n    # x_0 = (x_t - sigma * model_output) / (alpha - lambda * sigma^2)\n    denominator = sqrt_alpha - lambda_val * sqrt_one_minus_alpha * sqrt_one_minus_alpha\n    # clamp to avoid division by zero (should be positive)\n    denominator = denominator.clamp(min=1e-8)\n    pred_x0 = (x_t - sqrt_one_minus_alpha * model_output) / denominator\n    return pred_x0"
7}

Tool ResultStep 1

OK: Replaced lines 83..118 with 30 line(s) in diffusers-main/custom_train.py. Editable range: 83–112.

[Current file: diffusers-main/custom_train.py | editable: 83–112 | total: 486 lines]
    80| # ============================================================================
    81| # Prediction parameterization (EDITABLE REGION)
    82| # ============================================================================
    83  def compute_training_target(x_0, noise, timesteps, schedule):
    84      """Compute the training target: epsilon + lambda * sigma * x_0.
    85      
    86      Adds a small amount of x_0 signal to the standard epsilon prediction,
    87      which may help the model learn cleaner x_0 estimates while retaining
    88      the stable training dynamics of epsilon prediction.
    89      """
    90      sqrt_alpha = schedule["sqrt_alpha"][timesteps].view(-1, 1, 1, 1)
    91      sqrt_one_minus_alpha = schedule["sqrt_one_minus_alpha"][timesteps].view(-1, 1, 1, 1)
    92

AssistantStep 2edit

Tool Input

1{
2  "op": "replace",
3  "filename": "diffusers-main/custom_train.py",
4  "start_line": 83,
5  "end_line": 118,
6  "content": "def compute_training_target(x_0, noise, timesteps, schedule):\n    \"\"\"Compute the training target: epsilon + lambda * sigma * x_0.\n    \n    Adds a small amount of x_0 signal to the standard epsilon prediction,\n    which may help the model learn cleaner x_0 estimates while retaining\n    the stable training dynamics of epsilon prediction.\n    \"\"\"\n    sqrt_alpha = schedule[\"sqrt_alpha\"][timesteps].view(-1, 1, 1, 1)\n    sqrt_one_minus_alpha = schedule[\"sqrt_one_minus_alpha\"][timesteps].view(-1, 1, 1, 1)\n    # Hyperparameter lambda: weight of x_0 correction term\n    lambda_val = 0.1\n    # target = epsilon + lambda * sigma * x_0\n    target = noise + lambda_val * sqrt_one_minus_alpha * x_0\n    return target\n\n\ndef predict_x0(model_output, x_t, timesteps, schedule):\n    \"\"\"Recover predicted x_0 from model output.\n    \n    Inverse of compute_training_target with same lambda.\n    \"\"\"\n    sqrt_alpha = schedule[\"sqrt_alpha\"][timesteps].view(-1, 1, 1, 1)\n    sqrt_one_minus_alpha = schedule[\"sqrt_one_minus_alpha\"][timesteps].view(-1, 1, 1, 1)\n    lambda_val = 0.1\n    # x_0 = (x_t - sigma * model_output) / (alpha - lambda * sigma^2)\n    denominator = sqrt_alpha - lambda_val * sqrt_one_minus_alpha * sqrt_one_minus_alpha\n    # clamp to avoid division by zero (should be positive)\n    denominator = denominator.clamp(min=1e-8)\n    pred_x0 = (x_t - sqrt_one_minus_alpha * model_output) / denominator\n    return pred_x0\n\n\n# ============================================================================\n# Sampling — uses diffusers DDIMScheduler with predict_x0 bridge\n# ============================================================================"
7}

Tool ResultStep 2

ERROR: Lines 83..118 exceed the editable range. You may only edit lines 83–112.

[Current file: diffusers-main/custom_train.py | editable: 83–112 | total: 486 lines]
    80| # ============================================================================
    81| # Prediction parameterization (EDITABLE REGION)
    82| # ============================================================================
    83  def compute_training_target(x_0, noise, timesteps, schedule):
    84      """Compute the training target: epsilon + lambda * sigma * x_0.
    85      
    86      Adds a small amount of x_0 signal to the standard epsilon prediction,
    87      which may help the model learn cleaner x_0 estimates while retaining
    88      the stable training dynamics of epsilon prediction.
    89      """
    90      sqrt_alpha = schedule["sqrt_alpha"][timesteps].view(-1, 1, 1, 1)
    91      sqrt_one_minus_alpha = schedule["sqrt_one_minus_alpha"][timesteps].view(-1, 1, 1, 1)
    92      # Hyperparameter

AssistantStep 3test