Source-linked AI summary
One-Step Text Generation by Seq-Drifting
Jiayu Liu, Ruizhi Zhao, Tianyun Ji, Yee Whye Teh, Zhenya Huang, Ning Miao
TL;DR
Diffusion language models generate tokens in parallel but still need multiple sampling steps for high-quality text, leaving open whether a whole sequence can be generated in one pass. Seq-Drifting learns a noise-to-text map with context-dependent token support and drift over continuous token representations. It provides a competitive one-step operating point across generation tasks, with generative perplexity 36.01 on LM1B.
Problem
Diffusion language models generate tokens in parallel but still require multiple sampling steps for high-quality text, motivating the question of direct one-step sequence generation.
Source: §1 · p. 1Method
Seq-Drifting learns a one-step noise-to-text map by drifting continuous token representations toward context-dependent sets of plausible tokens.
Source: §1 · p. 2Results
Across unconditional generation, continuation, translation, summarization, and reasoning, Seq-Drifting provides a competitive one-step operating point and outperforms evaluated few-step baselines at a fraction of their inference cost, with 36.01 generative perplexity on LM1B.
Source: §1 · p. 2, §6 · p. 10Takeaways & Limitations
The results demonstrate the feasibility of directly learning a one-step text generator and point to a new direction for diffusion language models.
Source: §1 · p. 2, §6 · p. 10
Abstract
from arXiv · showhide
Diffusion language models generate tokens in parallel, but still require multiple sampling steps to produce high-quality text. In this paper, we investigate whether a model can learn to generate an entire sequence in a single forward pass. We propose Seq-Drifting, a framework that applies drifting to sequences of continuous token representations and directly learns a map from Gaussian noise to text. Unlike existing DLMs that derive the supervision at each position directly from the observed token in a training sequence, Seq-Drifting builds a drift field whose position-wise targets adapt to the current generated context. At each position, attraction guides each output toward a set of contextually plausible token representations, while repulsion discourages collapse across samples and repetition within sequences. The generator learns from this drift field during training and produces all tokens jointly in one pass at inference. Empirically, Seq-Drifting achieves a generative perplexity of 36.01 on LM1B in one step and performs competitively in both unconditional and conditional generation. Experiments on translation, summarization, and reasoning further demonstrate the applicability of the framework beyond open-ended generation. These results suggest that drifting over token sequences offers a promising path toward effective one-step text generation. Our code is available at https://github.com/jyliu-ai/Seq-Drifting.
1 INTRODUCTION
The paper asks whether text can be generated in one pass despite the multiple refinement steps used by diffusion language models. Seq-Drifting adapts drifting to token sequences, using context-dependent supervision to produce competitive one-step results.
1 INTRODUCTION
- Autoregressive decoding creates a sequence-length-growing latency bottleneck, while diffusion language models generate in parallel but still need multiple refinement steps for high-quality samples.The paper frames direct one-step generation from noise to text as the central question.Source: §1 · pp. 1–2
- Drifting learns a noise-to-data map through parameter updates rather than an inference-time trajectory, potentially enabling a single forward pass at convergence.The map can reach a fixed point when it matches the data distribution.Source: §1 · p. 2
- Text poses challenges for drifting because continuous updates can land between discrete tokens, embedding proximity may not preserve meaning, and sentence-level vectors leave no per-position targets.Mapping a sentence-level vector back to a faithful token sequence remains a difficult decoding problem.Source: §1 · p. 2
- Seq-Drifting uses context-dependent plausible-token sets to guide each position toward valid alternatives compatible with the generated context.The support sets couple choices across positions and guide the generator toward coherent sequences.Source: §1 · p. 2
- 36.01 generative perplexity on LM1B comes with an 11.2× wall-clock speedup over the strongest four-step distilled baseline, while outperforming several 1024-step DLMs.The paper also reports applicability to prefix-conditioned translation, summarization, and reasoning.Source: §1 · p. 2
2 RELATED WORK
Related work spans discrete and continuous diffusion language models, few-step distillation, and drifting. Seq-Drifting extends drifting to token sequences with context-dependent, per-position supervision for a direct one-step map.
2 RELATED WORK
- Discrete diffusion language models operate on categorical tokens, while continuous variants use token embeddings or simplex representations, but continuous methods still require many sampling steps.Per-position parallel prediction alone does not capture joint uncertainty when tokens are updated simultaneously.Source: §2 · p. 3
- Discrete and continuous DLMs differ in representation and supervision, while Seq-Drifting directly trains a one-step sequence map instead of reproducing a diffusion or flow trajectory.Its per-position support supplies plausible targets for the generator’s current outputs.Source: §2 · p. 3
- Few-step methods compress or replace an existing sampling trajectory, whereas drifting trains outputs through attraction and repulsion for a single forward pass at inference.Seq-Drifting extends drifting with context-dependent token support from corpus retrieval or a frozen language model.Source: §2 · p. 3
3 PRELIMINARIES
Drifting trains a generator by updating its outputs toward the data distribution until the drift field vanishes. Applying this idea to text requires per-position targets and geometry that respects discrete token choices.
3 PRELIMINARIES
- A one-step generator maps noise to a model distribution, and parameter updates move the same noise input’s output through a sample-specific drift.When the model and data distributions agree, the field vanishes and the model distribution is a fixed point of training.Source: §3 · p. 3
- The training loss regresses each generated output toward its stop-gradient drift target, so minimizing the loss drives the drift toward zero.This follows from the loss being the expected squared drift magnitude.Source: §3 · p. 3
- Kernel mean-shift combines attraction from positive data samples with repulsion from generated samples; these forces cancel when the distributions agree.The similarity kernel weights contributions from each set.Source: §3 · p. 3
- Text drifting needs context-matched token targets and directional repulsion, since observed continuations can misalign with generated contexts and radial separation may not change decoded tokens.The sequence field applies positive support per position and repulsion from other samples and other positions in the same sequence.Source: §3 · p. 4, Figure 2 · p. 4
4 SEQ-DRIFTING
Seq-Drifting generates per-position continuous token representations jointly, then applies context-dependent support, angular attraction and repulsion, and a bounded spherical update to train the one-step map.
4.1 SPHERICAL ONE-STEP GENERATOR
- A shared noise vector produces all token representations in one forward pass, which are normalized and decoded by cosine similarity to a frozen vocabulary embedding table.Conditional generation also supplies prefix embeddings through cross-attention.Source: §4.1 · p. 4, §4.5 · p. 6
4.2 CONTEXT-DEPENDENT TOKEN SUPPORT
- Each position receives a support set of plausible tokens matched to the generator’s current context, rather than a single fixed observed continuation.The default on-policy support comes from a frozen language model queried during training and is not needed at inference.Source: §4.2 · p. 5
4.3 ANGULAR MODE-SEEKING ATTRACTION
- Angular mode-seeking attraction weights supported tokens by proximity and pulls each output toward nearby candidates rather than their blurred centroid.Candidate-distance spread is normalized by its standard deviation, and temperature sharpens the kernel around nearby tokens.Source: §4.3 · p. 5
4.4 PER-POSITION ANGULAR REPULSION
- Per-position repulsion separates outputs from other samples and from other positions in the same sequence, thereby discouraging collapse and repetition.The two negative sets use the angular kernel; within-sequence repulsion targets repetition.Source: §4.4 · p. 5
4.5 GEODESIC UPDATE AND TRAINING
- The training update combines attraction and repulsions, projects the force onto the sphere’s tangent plane, and takes a bounded geodesic step to form a stop-gradient target.The arc length is capped to prevent overshooting, and the generator is trained against the resulting target.Source: §4.5 · p. 6
- Conditional training first uses an unconditional warm-up with a constant padding context, then replaces it with the real prefix to learn context dependence.The warm-up keeps the conditioning path active while the generator learns fluent text.Source: §4.5 · p. 6
5 EXPERIMENTS
Seq-Drifting is evaluated for unconditional and prefix-conditioned generation, with ablations, hyperparameter sweeps, and downstream tasks. The experiments report competitive generation quality at one pass and examine factors affecting its performance.
5.1 SETUP
- The evaluation compares few-step distilled and multi-step models on LM1B at length 128 and OpenWebText at length 1024, reporting steps, GPT-2 Large Gen-PPL, and unigram entropy.Each configuration uses 1,024 samples; the paper evaluates both from-scratch and pretrained-GPT-2 support models.Source: §5.1 · p. 6
5.2 UNCONDITIONAL GENERATION
- On LM1B, Seq-DriftingS outperforms the strongest four-step baseline and several 1024-step baselines; Seq-DriftingP reduces Gen-PPL relative to FMLM by 69.8% on LM1B and 24.2% on OpenWebText.Source: §5.2 · p. 7
5.3 CONDITIONAL GENERATION
- Both Seq-Drifting variants outperform all few-step distilled baselines in two conditional settings, and Seq-DriftingS is stronger on the 512-token output setting.Each setting uses a 64-token context; outputs are 64 tokens on LM1B and 512 on OpenWebText.Source: §5.3 · pp. 7–8, Table 1 · p. 7
5.4 ABLATIONS
- Ablations find spherical updates essential, task-matched support construction important, intra-sequence repulsion necessary to prevent repetition, and unconditional warm-up stabilizing conditional training.Euclidean updates let repulsion increase embedding norms and diverge; fixed corpus targets can cause oscillatory training in open-ended generation.Source: §5.4 · p. 8, Table 2 · p. 8
5.5 HYPERPARAMETERS
- Gen-PPL improves and then worsens across sweeps of repulsion strengths and attraction temperature; k = 4 collapses output, while larger support sets generally restore diversity and improve Gen-PPL.Cross-sample repulsion has a larger effect than intra-sequence repulsion; too-small temperature makes each position’s target nearly unique.Source: §5.5 · pp. 8–9, Figure 4 · p. 8
5.6 DOWNSTREAM TASK EVALUATION
- Seq-Drifting outperforms few-step baselines on translation and most summarization metrics, approaches Coconut on mathematical reasoning, and remains competitive with AR on ProofWriter at lower per-sample latency.A gap remains relative to multi-step results on translation and summarization; scaling the support model further improves one-step generation quality.Source: §5.6 · p. 9, Table 3 · p. 9, Table 4 · p. 9
6 CONCLUSION
Seq-Drifting combines context-dependent token supports and attraction–repulsion forces for one-step generation, with competitive results across several generation tasks and a remaining gap to the strongest multi-step systems.
6 CONCLUSION
- Across unconditional generation, conditional continuation, translation, summarization, and reasoning, Seq-Drifting offers a competitive one-step operating point and outperforms evaluated few-step baselines at a fraction of their inference cost.A remaining gap to the strongest multi-step systems motivates future work on stronger support models, richer semantic supervision, and improved token recovery.Source: §6 · p. 10
- Context-dependent support sets provide multiple plausible targets, while mode-seeking attraction, repulsion, and spherical geometry help preserve coherent and diverse outputs.Source: §6 · p. 10
AI USE STATEMENT
- The authors report that generative AI tools were used to edit the manuscript for readability and clarity, with all assisted text reviewed and revised by the authors.Source: AI USE STATEMENT · p. 10
A.1 GENERATOR ARCHITECTURE
The generator maps a shared noise vector into a sequence of token representations using a Transformer, with prefix conditioning available for conditional generation.
A.1 GENERATOR ARCHITECTURE
- A shared noise vector of dimension 128 is projected to T · D dimensions, reshaped to (T, D), and combined with learned positional embeddings.Source: §A.1 · p. 12
- The generator is a 12-layer pre-LN Transformer with width 768, 12 attention heads, and an FFN width of 3072.QKnorm and a LayerScale gate stabilize its attention and residual branches.Source: §A.1 · p. 12
- For conditional generation, conditioning token embeddings are supplied as a prefix and output positions access them through ungated cross-attention.Source: §A.1 · p. 12
A.2 A CONDITIONAL FIXED-POINT ANALYSIS
The appendix analyzes fixed-point conditions for Seq-Drifting, describes its training algorithm, and reports evaluation and implementation details across generation settings.
A.2 A CONDITIONAL FIXED-POINT ANALYSIS
- At matching generated and data distributions, the analysis checks the drift directly because Seq-Drifting’s per-position field is not anti-symmetric.In the mode-seeking limit, supported token embeddings have zero attraction, and attraction-relative rescaling makes repulsions vanish with it, yielding a fixed point under the stated conditions.Source: §A.2 · pp. 12–13
- At positive temperature, representation discrepancies and a finite-temperature correction can leave nonzero drift, but the analysis bounds it when these contributions are sufficiently small.The bound tends toward zero as temperature tends to zero under the stated support and uniqueness conditions.Source: §A.2 · p. 13
A.3 SEQ-DRIFTING ALGORITHM
- Figure 6 summarizes training with on-policy support sets from a frozen model: each iteration builds context-dependent supports, combines attraction and repulsion into spherical targets, then regresses the generator toward them.Optional prefixes enable conditional generation.Source: Figure 6 · p. 14, §A.3 · p. 14
B.1 SELF-BLEU
- Self-BLEU measures n-gram overlap among a model’s own generations; a fully mode-collapsed generator scores 1.0.Table 5 reports the metric for few-step distilled baselines at 1, 2, and 4 steps and for Seq-Drifting at one step.Source: §B.1 · p. 14, Table 5 · p. 15
B.2 SAMPLING TIME ACROSS STEP BUDGETS
- Sampling time grows with denoising-step count, while Seq-Drifting remains constant at one step, as shown for LM1B and OpenWebText.Figure 7 plots seconds per sample against a logarithmic sampling-step budget and marks Seq-Drifting with a dashed line.Source: §B.2 · p. 14, Figure 7 · p. 15
B.3 MULTI-STEP BASELINES
- The multi-step baseline tables cover unconditional and conditional generation at 1, 8, and 1024 steps, with dashes where released checkpoints or published reference results are unavailable.The appendix also notes unavailable public checkpoints for some baseline and dataset settings.Source: §B.3 · pp. 14–15, Table 6 · p. 16
B.4 ALTERNATIVE GEN-PPL EVALUATORS
- Unconditional Gen-PPL is recomputed with Pythia-1B and OPT-1.3B to test dependence on the GPT-2 Large evaluator, with other sampling settings unchanged.Table 8 reports the alternative-evaluator results for LM1B and OpenWebText.Source: §B.4 · p. 15
B.5 TRANSLATION AND SUMMARIZATION SETUP
- Translation uses 64-token source and target sequences, while XSum uses up to 1024 source tokens and generates 64-token summaries; Seq-Drifting uses task-specific autoregressive models trained from scratch as frozen support models.WMT14 is evaluated with corpus BLEU, and XSum with ROUGE-1, ROUGE-2, and ROUGE-L; outputs are compared with ground-truth references and autoregressive samples.Source: §B.5 · p. 16
B.6 REASONING IMPLEMENTATION DETAILS
The reasoning experiments specify distinct mathematical and logical tasks, their support construction and evaluation sets, and the model and baseline comparisons.
B.6 REASONING IMPLEMENTATION DETAILS
- Mathematical reasoning trains on GSM8K-Aug and evaluates out of domain on SVAMP and ASDiv, using ground-truth solution sequences as attraction supports.Source: §B.6 · p. 16
- Logical reasoning uses ProofWriter’s binary true/false subset, trains on combined D0–D5 training data, evaluates on the corresponding test split, and excludes unknown-labeled examples.Source: §B.6 · p. 16
- The reasoning setup uses a 0.5B-parameter Qwen2.5-architecture backbone and compares Seq-Drifting with autoregressive, non-autoregressive, and Coconut baselines using accuracy and wall-clock time per sample.Coconut feeds continuous thought representations into hidden states rather than emitting explicit chain-of-thought tokens.Source: §B.6 · p. 16
- The captions compare multi-step conditional-generation models across step budgets against single-pass Seq-Drifting using 64-token prefixes (64→64 on LM1B; 64→512 on OWT), and report unconditional Gen-PPL with Pythia-1B and OPT-1.3B.Gen-PPL is computed for LM1B (T=128) and OpenWebText (T=1024).Source: Table 7 · p. 17, Table 8 · p. 17
B.7 TRAINING DYNAMICS
The conditional runs improve after the warm-up, while off-policy training with fixed corpus targets oscillates and trends toward higher-entropy text with reduced coherence.
B.7 TRAINING DYNAMICS
- During the first 200k steps, unconditional warm-up with constant-token context brings coherent English and sharply lowers Gen-PPL; after conditioning starts, perplexity keeps falling.Figure 8 tracks Gen-PPL and unigram entropy through 300k training steps for the conditional runs.Source: §B.7 · pp. 17–18, Figure 8 · p. 18
B.8 OFF-POLICY POSITIVES
- Off-policy positives use retrieved real-sequence n-grams as support sets, leaving attraction, repulsions, and the geodesic update unchanged.Unlike on-policy targets, these targets are fixed by the data and do not follow the generator.Source: §B.8 · p. 18
- After τ reaches 0.1 at 10k steps, fixed-target off-policy training oscillates as entropy and Gen-PPL trend upward and global coherence declines.The cycle alternates between overscattering and reconsolidation, with each swing ending higher than the last.Source: §B.8 · p. 18
B.9 QUALITATIVE SAMPLES
The displayed single-pass samples include translation and arithmetic outputs, reasoning responses, and text continuations of uneven quality.
B.9 QUALITATIVE SAMPLES
- The examples are generated in a single forward pass and truncated for display.Source: §B.9 · p. 18
- The listed sample diagnostics are entropy 4.30 with Gen-PPL 36.01, and entropy 4.21 with Gen-PPL 93.81.Source: §B.9 · p. 19
- Two displayed continuations are fragmentary and incoherent, including one about a technology conference and one about a spokeswoman’s statement.Source: §B.9 · p. 19
- The translation example exactly matches the supplied reference: “We are proud of our performance, but we want to win every game.”Source: §B.9 · p. 20
- The arithmetic example answers the 12-student, 5-balloons-per-student question with 60.Source: §B.9 · p. 20
- The theory example states that Bob is nice and concludes “false” for the query “Bob is not nice.”Source: §B.9 · p. 20