Improve diffusion model sampling by planning content-adaptive denoising trajectories. Extract Diffusion DNA signatures quantifying per-stage difficulty, then apply graph planning to allocate computation to challenging generative phases.
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Improve diffusion model sampling by planning content-adaptive denoising trajectories. Extract Diffusion DNA signatures quantifying per-stage difficulty, then apply graph planning to allocate computation to challenging generative phases.
Chain-of-Trajectories: Graph-Based Trajectory Planning for Diffusion Models
Diffusion models use fixed sampling schedules regardless of content difficulty. Some generative phases require extensive refinement while others converge quickly, yet standard schedules waste computation by allocating equal effort uniformly. Chain-of-Trajectories (CoT) reformulates diffusion sampling as a graph planning problem by extracting Diffusion DNA—a low-dimensional signature quantifying per-stage denoising difficulty. This enables dynamic allocation of computational resources to challenging phases, improving output quality while reducing total computational cost.
The approach is train-free and applies to existing pre-trained diffusion models, requiring only inference-time trajectory planning.
Core Concept
Chain-of-Trajectories operates in three phases:
DNA Extraction — Analyze initial samples to compute per-stage denoising difficulty
Graph Construction — Build directed acyclic graph (DAG) of possible trajectories
The key insight: by treating sampling as a planning problem rather than fixed sequence execution, models can adapt to content characteristics dynamically.
Architecture Overview
Diffusion DNA Extractor — Compute per-timestep difficulty metrics from model uncertainty
Signature Aggregation — Combine timestep signals into stage-level estimates
Trajectory Graph Builder — Create DAG where nodes represent (stage, refinement_level) pairs
Cost Function — Compute per-edge cost based on DNA and refinement requirements
Graph Planner — Apply Dijkstra or A* to find optimal sampling path
Inference Pipeline — Execute planned trajectory with dynamic step allocation
Quality Validator — Measure output improvements vs standard fixed schedules
Implementation Steps
Start by implementing Diffusion DNA extraction from model predictions.
import torch
import torch.nn as nn
import numpy as np
from heapq import heappush, heappop
classDiffusionDNA:
():
.model = model
.num_stages = num_stages
.timesteps = torch.linspace(, , num_stages, dtype=torch.long)
() -> np.ndarray:
difficulties = []
t .timesteps:
torch.no_grad():
noise_pred = .model(x_t, t.unsqueeze())
uncertainty = ._compute_uncertainty(noise_pred, num_samples)
difficulties.append(uncertainty)
dna = np.array(difficulties)
dna = (dna - dna.()) / (dna.() - dna.() + )
dna
() -> :
predictions = []
_ (num_samples):
pred = .model.forward_with_dropout(prediction)
predictions.append(pred)
predictions = torch.stack(predictions)
uncertainty = predictions.var(dim=).mean().item()
uncertainty
() -> :
(dna[stage_idx])
"""Extract difficulty signatures from diffusion model."""
def
__init__
self, model, num_stages=10
self
self
self
0
999
def
extract_dna
self, x_t: torch.Tensor, num_samples=5
"""Compute difficulty signature for input."""
for
in
self
# Get model prediction at this timestep
with
self
0
# Compute uncertainty (model confidence)
# Use prediction variance as difficulty proxy
self
# Normalize to [0, 1]
min
max
min
1e-8
return
def
_compute_uncertainty
self, prediction: torch.Tensor,
num_samples: int = 5
float
"""Estimate model uncertainty."""
# Run multiple forward passes with dropout enabled
for
in
range
self
# Uncertainty as prediction variance
0
return
def
stage_difficulty
self, dna: np.ndarray, stage_idx: int
float
"""Get difficulty for a specific stage."""
return
float
Now implement the trajectory graph and planning algorithm.
classTrajectoryGraph:
"""DAG of possible denoising trajectories."""def__init__(self, num_stages=10, max_refinement=3):
self.num_stages = num_stages
self.max_refinement = max_refinement
# Nodes: (stage, refinement_level)self.nodes = [(s, r) for s inrange(num_stages)
for r inrange(max_refinement)]
self.edges = {}
self.costs = {}
defadd_edge(self, from_node: tuple, to_node: tuple, cost: float):
"""Add directed edge with cost."""if from_node notinself.edges:
self.edges[from_node] = []
self.edges[from_node].append(to_node)
self.costs[(from_node, to_node)] = cost
defbuild_from_dna(self, dna: np.ndarray, base_cost=1.0):
"""Construct graph using Diffusion DNA."""# Edges represent sampling transitionsfor stage inrange(self.num_stages - 1):
for ref_level inrange(self.max_refinement):
from_node = (stage, ref_level)
# Can transition to next stage (coarse pass)
to_node = (stage + 1, 0)
# Cost inversely related to difficulty (hard stages cost more)
difficulty = dna[stage]
cost = base_cost / (0.1 + difficulty) # Normalizedself.add_edge(from_node, to_node, cost)
# Can refine current stage (additional passes)if ref_level < self.max_refinement - 1:
to_node = (stage, ref_level + 1)
cost = difficulty * base_cost # Refine hard stages moreself.add_edge(from_node, to_node, cost)
deffind_optimal_path(self, start_node=(0, 0),
end_node=None) -> (list, float):
"""Find minimum-cost path using Dijkstra's algorithm."""if end_node isNone:
end_node = (self.num_stages - 1, self.max_refinement - 1)
# Dijkstra's algorithm
distances = {node: float('inf') for node inself.nodes}
distances[start_node] = 0
predecessors = {node: Nonefor node inself.nodes}
pq = [(0, start_node)]
while pq:
current_dist, current_node = heappop(pq)
if current_node == end_node:
# Reconstruct path
path = []
node = end_node
while node isnotNone:
path.append(node)
node = predecessors[node]
path.reverse()
return path, current_dist
if current_dist > distances[current_node]:
continue# Explore neighborsif current_node inself.edges:
for next_node inself.edges[current_node]:
edge_cost = self.costs[(current_node, next_node)]
new_dist = current_dist + edge_cost
if new_dist < distances[next_node]:
distances[next_node] = new_dist
predecessors[next_node] = current_node
heappush(pq, (new_dist, next_node))
return [], float('inf') # No path found
Implement the sampling executor that follows planned trajectories.
classAdaptiveDiffusionSampler:
"""Sample following computed trajectory."""def__init__(self, model, dna_extractor: DiffusionDNA):
self.model = model
self.dna_extractor = dna_extractor
defsample_with_trajectory(self, initial_noise: torch.Tensor,
trajectory_graph: TrajectoryGraph,
verbose=False) -> torch.Tensor:
"""Execute sampling following optimal trajectory."""# Extract DNA
dna = self.dna_extractor.extract_dna(initial_noise)
# Build and plan trajectory
trajectory_graph.build_from_dna(dna)
path, total_cost = trajectory_graph.find_optimal_path()
if verbose:
print(f"Planned trajectory with cost {total_cost:.3f}")
print(f"Path: {path}")
# Execute sampling following trajectory
x_t = initial_noise.clone()
current_stage = 0for node in path:
stage, refinement = node
# Skip backwards in trajectory (shouldn't happen with proper planning)if stage < current_stage:
continue# Move to this stage with refinement passes
target_t = self.dna_extractor.timesteps[stage]
# Multiple denoising steps at this stage if refined
num_steps = 1 + refinement
for step inrange(num_steps):
# Denoise one stepwith torch.no_grad():
noise_pred = self.model(x_t, target_t.unsqueeze(0))
# Update based on noise prediction
x_t = self._denoise_step(x_t, noise_pred, target_t)
current_stage = stage
return x_t
def_denoise_step(self, x_t: torch.Tensor, noise_pred: torch.Tensor,
t: torch.Tensor) -> torch.Tensor:
"""Single denoising step (simplified)."""# Simplified DDIM step
alpha_t = torch.sqrt(1 - t.float() / 1000) # Approximate
x_t_next = alpha_t * x_t + (1 - alpha_t) * noise_pred
return x_t_next
defsample_standard(self, initial_noise: torch.Tensor,
num_steps=50) -> torch.Tensor:
"""Baseline: standard fixed-schedule sampling."""
x_t = initial_noise.clone()
timesteps = torch.linspace(999, 0, num_steps, dtype=torch.long)
for t in timesteps:
with torch.no_grad():
noise_pred = self.model(x_t, t.unsqueeze(0))
x_t = self._denoise_step(x_t, noise_pred, t)
return x_t
defbenchmark_trajectory_planning(model, test_images, num_trials=10):
"""Compare trajectory-planned vs standard sampling."""
dna_extractor = DiffusionDNA(model)
sampler = AdaptiveDiffusionSampler(model, dna_extractor)
trajectory_graph = TrajectoryGraph(num_stages=10, max_refinement=3)
results = {'trajectory': [], 'standard': []}
for img in test_images[:num_trials]:
# Trajectory-planned sampling
x_t = torch.randn_like(img)
output_trajectory = sampler.sample_with_trajectory(x_t, trajectory_graph)
# Standard sampling
output_standard = sampler.sample_standard(x_t)
# Evaluate quality (using proxy metrics)
quality_trajectory = compute_sample_quality(output_trajectory, img)
quality_standard = compute_sample_quality(output_standard, img)
results['trajectory'].append(quality_trajectory)
results['standard'].append(quality_standard)
avg_trajectory = np.mean(results['trajectory'])
avg_standard = np.mean(results['standard'])
print(f"Trajectory-planned: {avg_trajectory:.3f}")
print(f"Standard: {avg_standard:.3f}")
print(f"Improvement: {(avg_trajectory - avg_standard) / avg_standard:.1%}")
return results
Practical Guidance
Hyperparameters and When to Use:
Number of stages 8-15; more stages provide finer control but slower planning
Maximum refinement levels 2-4; higher refinement allows concentrated computation
Base cost 1.0 works as default; adjust based on desired output quality vs latency tradeoff
Use when content diversity is high (different images have different difficulty profiles)
Particularly effective for high-resolution generation where efficiency matters
When NOT to use:
For real-time applications where planning overhead exceeds benefits
For batch processing with homogeneous content (fixed schedules are simpler)
With models that don't expose uncertainty estimates (DNA extraction won't work)
Common Pitfalls:
DNA extraction being noisy or unreliable; use multiple samples to average uncertainty
Planning becoming too aggressive, skipping important denoising steps; include constraints
Trajectories becoming too complex, adding overhead; limit graph size
Difficulty metrics not correlating with actual sample quality; calibrate metrics on validation set
