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t3d-trajectory-distillation Accelerate diffusion language models from many to few generation steps using trajectory self-distillation. Collect clean-noisy state pairs along teacher trajectories, apply reverse-KL mode-seeking distillation, and weight losses by decoding order to prioritize early predictions where cascading errors compound.
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name t3d-trajectory-distillation title T3D: Few-Step Diffusion LMs via Trajectory Self-Distillation version 0.0.2 engine skillxiv-v0.0.2-claude-opus-4.6 license MIT url https://arxiv.org/abs/2602.12262 keywords ["Diffusion Language Models","Distillation","Few-Step Generation","Self-Supervision","Mode-Seeking"] description Accelerate diffusion language models from many to few generation steps using trajectory self-distillation. Collect clean-noisy state pairs along teacher trajectories, apply reverse-KL mode-seeking distillation, and weight losses by decoding order to prioritize early predictions where cascading errors compound.
T3D: Few-Step Diffusion LMs via Trajectory Self-Distillation
Problem Context
Diffusion language models require many sampling steps (25-50+) for high-quality generation. Few-step variants are needed for deployment, but naive training on random corruption schedules causes train-test mismatch: inference uses confidence-based schedules while training sees uniform random masking. T3D solves this by collecting trajectory pairs from teacher's actual inference schedule and using mode-seeking distillation.
Core Concept
T3D operates in two phases: (1) collect (clean, intermediate) state pairs along teacher trajectories during inference, (2) train student via reverse-KL objective that promotes mode-seeking (concentrating on high-probability outputs) with path-consistency weighting. This addresses the multimodal posterior problem where forward-KL spreads mass across modes.
Architecture Overview
Trajectory collection : Run full teacher steps, save clean (x₀) and intermediate (xₜ) statesReverse-KL distillation : Use discriminative KL divergence promoting mode concentrationPath-consistency weighting : Weight token losses by decoding order (early tokens > later tokens)Mode-seeking loss : Prevent mode-covering behavior in highly multimodal posteriorsFew-step inference : Student generates quality outputs in 2-4 steps
Implementation
Step 1: Collect trajectory pairs from teacher
import torch
import torch.nn.functional as F
from typing import List , Tuple , Dict
class TrajectoryCollector :
"""Collect (clean, corrupted) state pairs from teacher inference."""
def __init__ (
self,
teacher_model,
num_collection_steps: int = 50 ,
corruption_schedule: str = 'linear'
):
self .teacher_model = teacher_model
self .num_collection_steps = num_collection_steps
self
def
get_corruption_schedule
self, num_steps: int
"""
Get corruption level schedule for diffusion.
Args:
num_steps: Number of denoising steps
Returns:
sigma_t: Noise level at each step [num_steps]
"""
if
self
'linear'
return
1.0
0.0
elif
self
'cosine'
0
1
return
2
else
raise
f"Unknown schedule: {self.corruption_schedule} "
def
corrupt_tokens
self,
clean_tokens: torch.Tensor,
sigma: float ,
mask_token_id: int
"""
Add noise by masking tokens.
Args:
clean_tokens: Original tokens
sigma: Noise level (0-1, where 1=all masked)
mask_token_id: Mask token ID
Returns:
corrupted: Noisy version with sigma fraction masked
"""
int
len
len
return
def
collect_trajectories
self,
prompt: str ,
num_trajectories: int = 4
List
Dict
str
"""
Generate trajectories and collect (clean, intermediate) pairs.
Args:
prompt: Input prompt
num_trajectories: Number of trajectories to collect
Returns:
trajectories: List of {clean: Tensor, intermediates: List[Tensor]}
"""
self
self
for
in
range
self
50
for
in
enumerate
self
self
'clean'
'intermediates'
'schedule'
return
Step 2: Implement reverse-KL distillation objective class ReverseKLDistillation :
"""Reverse-KL (mode-seeking) distillation for few-step training."""
def __init__ (
self,
teacher_model,
student_model,
temperature: float = 1.0
):
self .teacher_model = teacher_model
self .student_model = student_model
self .temperature = temperature
def compute_teacher_logits (
self,
corrupted_tokens: torch.Tensor,
clean_tokens: torch.Tensor,
sigma: float
) -> torch.Tensor:
"""Get teacher's predicted distribution for clean tokens."""
with torch.no_grad():
teacher_logits = self .teacher_model.forward(
corrupted_tokens,
step=sigma,
return_logits=True
)
return teacher_logits
def compute_reverse_kl_loss (
self,
student_logits: torch.Tensor,
teacher_logits: torch.Tensor,
clean_tokens: torch.Tensor
) -> torch.Tensor:
"""
Compute reverse-KL loss: E_q[log q - log p].
Promotes mode concentration on teacher's high-probability outputs.
q = student (learner), p = teacher (reference)
"""
student_log_probs = F.log_softmax(student_logits / self .temperature, dim=-1 )
teacher_log_probs = F.log_softmax(teacher_logits / self .temperature, dim=-1 )
student_probs = F.softmax(student_logits / self .temperature, dim=-1 )
student_samples = torch.multinomial(
student_probs.view(-1 , student_probs.shape[-1 ]),
num_samples=1
).squeeze(-1 )
kl_loss = (
student_log_probs[range (len (clean_tokens)), student_samples] -
teacher_log_probs[range (len (clean_tokens)), student_samples]
).mean()
return kl_loss
def compute_mode_seeking_loss (
self,
student_logits: torch.Tensor,
teacher_logits: torch.Tensor,
clean_tokens: torch.Tensor
) -> torch.Tensor:
"""
Mode-seeking objective: penalize student spreading mass.
Uses reverse-KL which avoids mode-covering behavior.
"""
student_probs = F.softmax(student_logits, dim=-1 )
teacher_probs = F.softmax(teacher_logits, dim=-1 )
student_log_probs = F.log_softmax(student_logits, dim=-1 )
kl_per_position = (
student_probs *
(student_log_probs - F.log_softmax(teacher_logits, dim=-1 ))
).sum (dim=-1 )
return kl_per_position.mean()
Step 3: Path-consistency weighting class PathConsistencyWeighting :
"""Weight losses by token decoding order."""
@staticmethod
def compute_order_weights (
seq_len: int ,
schedule: torch.Tensor,
order: str = 'confidence'
) -> torch.Tensor:
"""
Compute per-token loss weights based on decoding order.
Early tokens (where cascading errors start) get higher weight.
Args:
seq_len: Sequence length
schedule: Corruption schedule
order: 'confidence' (teacher confidence order) or 'sequential'
Returns:
weights: [seq_len] weight for each position
"""
if order == 'sequential' :
weights = torch.linspace(1.0 , 0.3 , seq_len)
elif order == 'confidence' :
confidence_ranks = torch.arange(seq_len, dtype=torch.float32)
weights = (seq_len - confidence_ranks) / seq_len
else :
weights = torch.ones(seq_len)
return weights
@staticmethod
def apply_path_consistency_loss (
loss_per_position: torch.Tensor,
weights: torch.Tensor
) -> torch.Tensor:
"""Weight loss by position importance."""
weighted_loss = (loss_per_position * weights).mean()
return weighted_loss
Step 4: Full training step with distillation class T3DTrainer :
"""Trajectory-based few-step distillation trainer."""
def __init__ (
self,
teacher_model,
student_model,
optimizer,
num_student_steps: int = 4
):
self .teacher_model = teacher_model
self .student_model = student_model
self .optimizer = optimizer
self .num_student_steps = num_student_steps
self .collector = TrajectoryCollector(teacher_model)
self .kl_distiller = ReverseKLDistillation(teacher_model, student_model)
self .path_weighting = PathConsistencyWeighting()
def training_step (
self,
prompt: str ,
num_trajectories: int = 4
) -> Dict [str , float ]:
"""
Single training step on trajectories.
Args:
prompt: Input prompt
num_trajectories: Trajectories to collect and train on
Returns:
metrics: Loss and auxiliary metrics
"""
trajectories = self .collector.collect_trajectories(
prompt, num_trajectories=num_trajectories
)
total_loss = 0.0
num_samples = 0
for traj in trajectories:
clean_tokens = traj['clean' ]
intermediates = traj['intermediates' ]
schedule = traj['schedule' ]
path_weights = self .path_weighting.compute_order_weights(
len (clean_tokens), schedule, order='confidence'
)
num_train_steps = len (schedule) // max (1 , len (schedule) // self .num_student_steps)
for step_idx in range (0 , len (schedule), num_train_steps):
corrupted = intermediates[step_idx]
sigma = schedule[step_idx]
student_logits = self .student_model.forward(
corrupted, step=sigma.item(), return_logits=True
)
teacher_logits = self .kl_distiller.compute_teacher_logits(
corrupted, clean_tokens, sigma.item()
)
kl_loss = self .kl_distiller.compute_mode_seeking_loss(
student_logits, teacher_logits, clean_tokens
)
weighted_loss = self .path_weighting.apply_path_consistency_loss(
kl_loss.view(-1 ), path_weights
)
self .optimizer.zero_grad()
weighted_loss.backward()
torch.nn.utils.clip_grad_norm_(
self .student_model.parameters(), 1.0
)
self .optimizer.step()
total_loss += weighted_loss.item()
num_samples += 1
avg_loss = total_loss / max (1 , num_samples)
return {'loss' : avg_loss}
Step 5: Few-step inference and evaluation def generate_few_step (
student_model,
prompt: str ,
num_steps: int = 4 ,
schedule: str = 'cosine'
) -> torch.Tensor:
"""
Generate with few-step student model.
Args:
student_model: Distilled few-step model
prompt: Input prompt
num_steps: Number of generation steps (2-4)
schedule: Corruption schedule
Returns:
generated_tokens: Final prediction
"""
if schedule == 'cosine' :
sigmas = torch.linspace(1.0 , 0.0 , num_steps)
else :
sigmas = torch.linspace(1.0 , 0.0 , num_steps)
seq_len = 128
corrupted = torch.full((seq_len,), student_model.mask_token_id)
for step_idx, sigma in enumerate (sigmas):
logits = student_model.forward(corrupted, step=sigma.item(), return_logits=True )
probs = F.softmax(logits, dim=-1 )
corrupted = torch.multinomial(probs, num_samples=1 ).squeeze(-1 )
return corrupted
def evaluate_few_step_quality (
student_model,
teacher_model,
test_prompts: List [str ],
verifier,
num_steps: int = 4
) -> Dict [str , float ]:
"""Benchmark few-step vs full student performance."""
few_step_scores = []
full_step_scores = []
for prompt in test_prompts:
few_tokens = generate_few_step(student_model, prompt, num_steps=num_steps)
few_text = student_model.decode(few_tokens)
few_score = verifier(few_text)
full_tokens = teacher_model.generate(prompt, num_steps=50 )
full_text = teacher_model.decode(full_tokens)
full_score = verifier(full_text)
few_step_scores.append(few_score)
full_step_scores.append(full_score)
return {
'few_step_accuracy' : sum (few_step_scores) / len (few_step_scores),
'full_step_accuracy' : sum (full_step_scores) / len (full_step_scores),
'speedup' : 50 / num_steps
}
Practical Guidance When to use : Diffusion language models needing deployment-ready few-step variants; trading some quality for 10-15× speedup
num_student_steps : 2-4 (speedup-quality tradeoff)temperature : 1.0-1.5 (higher = softer distributions)path_consistency_order : 'confidence' (early predictions matter more)num_collection_trajectories : 4-8 per batch
Addresses train-test mismatch via trajectory collection
Mode-seeking prevents spread across multiple outputs
Path-consistency weighting prioritizes early predictions
Maintains quality under aggressive step reduction
Reverse-KL can underflow on very multimodal tasks
Path weights too extreme → ignores later predictions
Too few trajectories → limited training signal
Not validating that early predictions actually cascade errors
Scaling : Linear in number of trajectories collected.
Reference Paper: https://arxiv.org/abs/2602.12262
Related work: Diffusion models, distillation, few-step inference, mode-seeking losses
Benchmarks: Text generation, code synthesis, reasoning tasks
