Scaling Diffusion Language Models via Adaptation from Autoregressive Models

## Abstract

Abstract Diffusion Language Models (DLMs) have emerged as a promising new paradigm for text generative modeling, potentially addressing limitations of autoregressive (AR) models. However, current DLMs have been studied at a smaller scale compared to their AR counterparts and lack fair comparison on language modeling benchmarks. Additionally, training diffusion models from scratch at scale remains challenging.
Given the prevalence of open-source AR language models, we propose adapting these models to build text diffusion models. We demonstrate connections between AR and diffusion modeling objectives and introduce a simple continual pre-training approach for training diffusion models.
Through systematic evaluation on language modeling, reasoning, and commonsense benchmarks, we show that we can convert AR models ranging from 127M to 7B parameters (GPT2 and LLaMA) into diffusion models DiffuGPT and DiffuLLaMA, using less than 200B tokens for training. Our experimental results reveal that these models outperform earlier DLMs and are competitive with their AR counterparts.
We release a suite of DLMs (with 127M, 355M, and 7B parameters) capable of generating fluent text, performing in-context learning, filling in the middle without prompt re-ordering, and following instructions 1 1 1 https://github.com/HKUNLP/DiffuLLaMA .

## 1 Introduction

Large language models (LLMs) have ushered in a new era of artificial intelligence, demonstrating remarkable capabilities in generating high-quality text, in-context learning, and following complex instructions (OpenAI, ; Touvron et al., ). These advancements are primarily rooted in the scaling up of autoregressive (AR) language models. During both training and inference, these models leverage vast datasets and billions of parameters, employing a strict left-to-right sequential process for memorization and generation. This approach has resulted in the emergence of intelligence capable of tackling diverse tasks (Wei et al., ; Hoffmann et al., ). However, the ultimate upper limit of intelligence achievable through this paradigm remains an open question. While AR mechanisms form the foundation of current LLMs, they are not without limitations (Lin et al., ). Notable challenges include difficulties in future planning (Bachmann & Nagarajan, ; Hu* et al., ; Xie et al., ) and self-correction (Huang et al., ). These constraints have spurred researchers to explore alternative architectures for next-generation LLMs.

A compelling direction in current research focuses on the development of text diffusion models (Li et al., ). Building upon the rapid evolution of diffusion models in various domains (Ho et al., ; Nichol & Dhariwal, ; Ramesh et al., ), innovative text diffusion models (Li et al., ; Lou et al., ) have opened up new possibilities for text generation. A unifying insight across these models is the potential of diffusion language models (DLMs) for controllable (Venkatraman et al., ), any-order, and parallel text generation (Gong et al., ). Notably, DLMs exhibit promising capabilities in intermediate token correction (Ye et al., ) and global planning (Zhang et al., ), thereby addressing key limitations inherent in the AR approach.

Despite the promising potential of text diffusion models, the relatively small model size limits the competitiveness of DLMs compared to AR models. Existing state-of-the-art DLMs such as Plaid 1B (Gulrajani & Hashimoto, ) and SEDD (Lou et al., ) are relatively small in scale (127M-1B parameters) and under-trained, with less than 400B tokens of training data. This substantial gap in scale prevents fair comparisons with larger AR language models on many advanced capabilities and tasks, such as chain-of-thought reasoning abilities on complex mathematical benchmarks. However, pre-training at such a scale is extremely resource-intensive, and the challenge is even more pronounced for diffusion models. These models lack the computational optimizations that have been developed for LLMs (Samragh et al., ) and require significantly more resources than their AR counterparts, as noted by Gulrajani & Hashimoto ().

Given these scaling challenges, pre-trained LLMs emerge as an invaluable resource that we can leverage, considering the extensive computational efforts already invested in their development. This strategy aligns with recent trends where new models are scaled up or adapted to new architectures using existing LLMs (Wang et al., ; Zhang et al., ). However, building DLMs through adaptation from AR models is non-trivial due to fundamental differences in their language modeling objectives. Two key distinctions present significant hurdles. First, AR models employ causal masking to prevent future information leakage, whereas diffusion models utilize bi-directional attention masks. Second, an AR LM processes clean inputs to predict subsequent tokens at each step, while a diffusion model operates on noisy inputs to predict their denoised versions.

To overcome these challenges, we propose a simple adaptation approach that bridges these discrepancies. We unify their modeling objectives (§3.2) and address the architectural differences by breaking the causal masking bias in AR models through attention mask annealing (§3.3). Additionally, we inherit the shift operation from AR models (§3.3). This streamlined adaptation recipe enables us to construct a pre-trained DLM that can effectively compete in the arena of LLMs.
Building on this approach, we leverage the FineWeb (Penedo et al., ) and SlimPajama (Soboleva et al., ) pre-training corpora to continue training small and medium-sized DLMs based on GPT2 (Brown et al., ), and further scale up to a 7B model based on LLaMA2 (Touvron et al., ).

Our experiments provide a comprehensive comparison between AR LMs and DLMs across language modeling, reasoning, and infilling tasks. The evaluation encompasses diverse settings, including zero-shot, few-shot, and fine-tuning scenarios, addressing the limitations of relying solely on perplexity in previous works (Shi et al., ). Our contributions and empirical findings include:

- •
We demonstrate that by narrowing the gap between AR models and DLMs, it is possible to convert 127M-7B AR models (GPT2 and LLaMA2) into DiffuGPT and DiffuLLaMA with training on less than 200B tokens. Notably, DiffuGPT outperforms GPT2 in most tasks.
- •
We
scale DLMs to 7B parameters, greatly expanding the expertise compared to smaller-scale diffusion models. DiffuLLaMA emerges as the state-of-the-art DLM, exhibiting in-context learning, code generation, and strong infilling capabilities. Its generation speed is competitive with AR counterparts for unconditionally generating $1024$ tokens using $256$ diffusion timesteps.
- •
We provide a comprehensive benchmark for DLMs and release our adapted diffusion models (127M, 355M and 7B) along with open-source adaptation code, efficient fine-tuning scripts, and evaluation toolkits.

## 2 Preliminary and Notation

Diffusion models (Sohl-Dickstein et al., ; Song & Ermon, ; Ho et al., ; Song et al., ) are latent variable generative models characterized by a forward and a reverse Markov process. We denote $\mathbf{x}_{0}\sim p_{data}(\mathbf{x}_{0})$ as the variable following the data distribution, and $\mathbf{x}_{t}\sim q(\mathbf{x}_{t})$ as the noisy variable of $\mathbf{x}_{0}$ at time $t$, where the maximum time is $T$. The forward process $q(\mathbf{x}_{1:T}|\mathbf{x}_{0})=\prod_{t=1}^{T}q(\mathbf{x}_{t}|\mathbf{x}_
{t-1})$ corrupts the initial data $\mathbf{x}_{0}$ into a sequence of increasingly noisy variables $\mathbf{x}_{1:T}$. Accordingly, the backward Markov process models the joint probability as $p_{\theta}(\mathbf{x}_{0:T})=p_{\theta}(\mathbf{x}_{T})\prod_{t=1}^{T}p_{
\theta}(\mathbf{x}_{t-1}|\mathbf{x}_{t})$, which gradually denoises $\mathbf{x}_{t}$ to reconstruct the original data $\mathbf{x}_{0}$. Parameters $\theta$ are learned by minimizing the negative log-likelihood of $\mathbf{x}_{0}$, which can be optimized through the evidence lower bound (ELBO),

$$ $-\log p_{\theta}(\mathbf{x}_{0})\leq\mathbb{E}_{q(\mathbf{x}_{1}|\mathbf{x}_{0 })}[-\log p_{\theta}(\mathbf{x}_{0}|\mathbf{x}_{1})]+D_{\mathrm{KL}}(q(\mathbf {x}_{T}|\mathbf{x}_{0})||p_{\theta}(\mathbf{x}_{T}))+\mathcal{L}_{T},$ (1) $$

with $\mathcal{L}_{T}=\sum_{t=2}^{T}\mathbb{E}_{q(\mathbf{x}_{t}|\mathbf{x}_{0})}[D_
{\mathrm{KL}}(q(\mathbf{x}_{t-1}|\mathbf{x}_{t},\mathbf{x}_{0})||p_{\theta}(
\mathbf{x}_{t-1}|\mathbf{x}_{t}))]$.
For continuous text diffusion (Li et al., ; Gong et al., ), at each forward step, perturbations are applied according to $q(\mathbf{x}_{t}|\mathbf{x}_{t-1})=\mathcal{N}(\mathbf{x}_{t};\sqrt{1-\beta_{t
}}\mathbf{x}_{t-1},{\beta}_{t}\mathbf{I})$, where $\beta_{t}\in(0,1)$ represents different scales across time steps such that $\mathbf{x}_{T}\sim\mathcal{N}(0,\mathbf{I})$.
In the case of discrete denoising models (Ho et al., ; Austin et al., ; Zheng et al., ), the forward process is defined as a categorical distribution $q(\mathbf{x}_{t}|\mathbf{x}_{t-1})=\text{Cat}(\bm{x}_{t};\bm{Q}_{t}^{\top}\bm{
x}_{t-1})$, where each $\mathbf{x}_{t}\in\{0,1\}^{K}$ is a one-hot vector with vocabulary size $K$, $\bm{Q}_{t}\in[0,1]^{K\times K}$ is the transition matrix, and each entry $[\bm{Q}_{t}]_{ij}$ denotes the probability of transition from the state $i$ to $j$. We build on the formulation of absorbing discrete diffusion (Austin et al., ), which specifies $\bm{Q}_{t}=(1-\beta_{t})I+\beta_{t}\mathbf{1}\bm{m}^{\top}$. We denote $\mathbf{1}$ as an all-one vector of size $K$ and $\bm{m}$ as the one-hot encoding of a special [MASK] token in the vocabulary.
Therefore, the transition matrix, $\bm{Q}_{t}$ indicates that with probability $1-\beta_{t}$, $\bm{x}_{t}$ remains unchanged; otherwise, it transitions to $\bm{m}$, becoming absorbed into [MASK].
Letting $\bm{\overline{Q}}_{t}\coloneqq\prod_{i=1}^{t}\bm{Q}_{i}=\alpha_{t}I+(1-\alpha_
{t})\mathbf{1}\bm{m}^{\top}$ and $\alpha_{t}\coloneqq\prod_{i=1}^{t}(1-\beta_{t})$, the distribution of $\bm{x}_{t}$ conditional on $\bm{x}_{0}$ is given by

$$ $q(\bm{x}_{t}|\bm{x}_{0})=\text{Cat}(\bm{x}_{t};\bm{\overline{Q}}_{t}^{\top}\bm {x}_{0})=\alpha_{t}I\bm{x}_{0}+(1-\alpha_{t})\bm{m}\mathbf{1}^{\top}\bm{x}_{0} =\alpha_{t}\bm{x}_{0}+(1-\alpha_{t})\bm{m},$ (2) $$

since $\bm{x}_{0}$ is a one-hot vector and thus $\mathbf{1}^{\top}\bm{x}_{0}=1$. We expect $\alpha_{T}$ to approach 0 0 such that the full noise data $\bm{x}_{T}$ equals $\bm{m}$ with probability $1$.

The discrete time representation of $t\in[0,T]$, restricts $\bm{x}_{t}$ to fixed noise ratios.
To avoid this bias and enable sampling from any noisy representation, we use continuous-time sampling, allowing $t$ to span any point within $[0,1]$  (Kingma et al., ; Shi et al., ; Zhao et al., ; Ou et al., ).
Continuous-time sampling is equivalent to dividing $[0,1]$ into $T$ intervals and where $T\rightarrow\infty$.
For any $0\leq s<t\leq 1$, the forward process generalizes to $q(\mathbf{x}_{t}|\mathbf{x}_{s})$. We will use this continuous-time notation in the following sections.

## 3 Model

Figure: Figure 1: The overview of our approach to adapt autoregressive (AR) models to diffusion models. Left: The shift operation in AR models enables the output layer $h_{i}$ to approximate the distribution of next tokens $x_{i+1}$ in hidden representations through the cross entropy (CE) loss. Middle: We remove the causal mask gradually during training eventually making our model bi-directional. Right: inside the diffusion models we shift the logits to compute the loss with the next token (i.e., the loss on $h_{i}$ would be with respect to $x_{i+1}$), while perceptually, the diffusion models are still functioning as recovering the original signals (since $h_{i}$ corresponds to $x_{i+1}$ in AR loss).
Refer to caption: x1.png

We begin by formulating the continuous-time discrete diffusion process (§3.1) and establishing a connection between the discrete diffusion and autoregressive objectives (§3.2). Based on this equivalence, we propose an adaptation approach (§3.3) and a sampling algorithm (§3.4) for diffusion models adapted from AR models. The whole process is illustrated in Figure 1.

### 3.1 Continuous-time Discrete Diffusion Processes

Following Eq.2 and $q(\bm{x}_{t}|\bm{x}_{0})=\sum_{\bm{x}_{s}}q(\bm{x}_{t}|\bm{x}_{s})q(\bm{x}_{s}
|\bm{x}_{0})$, the forward transition distribution between arbitrary points $s<t$ can be derived as

$$ $q(\bm{x}_{t}|\bm{x}_{s})=\text{Cat}(\bm{x}_{t};\bm{\overline{Q}}_{s|t}^{\top} \bm{x}_{s})=\frac{\alpha_{t}}{\alpha_{s}}\bm{x}_{s}+(1-\frac{\alpha_{t}}{ \alpha_{s}})\bm{m},$ (3) $$

with $\bm{\overline{Q}}_{s|t}\coloneqq\bm{\overline{Q}}_{s}^{-1}\bm{\overline{Q}}_{t
}=\frac{\alpha_{t}}{\alpha_{s}}I+(1-\frac{\alpha_{t}}{\alpha_{s}})\mathbf{1}
\bm{m}^{\top}$. The corresponding backward transition distribution conditional on $\bm{x}_{0}$ is also available in closed form,

$$ $q(\bm{x}_{s}|\bm{x}_{t},\bm{x}_{0})=\frac{q(\bm{x}_{t}|\bm{x}_{s})q(\bm{x}_{s} |\bm{x}_{0})}{q(\bm{x}_{t}|\bm{x}_{0})}=\begin{cases}\frac{\alpha_{s}-\alpha_{ t}}{1-\alpha_{t}}\bm{x}_{0}+\frac{1-\alpha_{s}}{1-\alpha_{t}}\bm{m}&\text{if } \bm{x}_{t}=\bm{m},\\ \bm{x}_{0}&\text{if }\bm{x}_{t}\neq\bm{m}.\\ \end{cases}$ (4) $$

In discrete diffusion processes, we aim to approximate the backward transition distribution $q(\bm{x}_{s}|\bm{x}_{t},\bm{x}_{0})$ using a denoising model $p_{\theta}(\bm{x_{s}}|\bm{x}_{t},f_{\theta}(\bm{x}_{t}))$, where $f_{\theta}(\bm{x}_{t})$, an approximation of $\bm{x}_{0}$, is usually the output of neural networks such as a transformer (Vaswani et al., ). We can define the denoising model to have a similar form of backward transitions as $p_{\theta}(\bm{x_{s}}|\bm{x}_{t})=\frac{\alpha_{s}-\alpha_{t}}{1-\alpha_{t}}f_
{\theta}(\bm{x}_{t})+\frac{1-\alpha_{s}}{1-\alpha_{t}}\bm{m}$. According to the training objective in Eq.1, the KL-divergence of $\mathcal{L}_{T}$ at each step $t$ can be simplified to a reweighted cross-entropy function,

$$ $D_{\mathrm{KL}}(q(\bm{x}_{s}|\bm{x}_{t},\bm{x}_{0})||p_{\theta}(\bm{x}_{s}|| \bm{x}_{t}))=-\frac{\alpha_{s}-\alpha_{t}}{1-\alpha_{t}}\delta_{\bm{x}_{t},\bm {m}}\bm{x}_{0}^{\top}\log f_{\theta}(\bm{x}_{t}),$ (5) $$

where $\delta_{a,b}$ is the indicator function for $a=b$. If we take the limit and let $T\rightarrow\infty$, the first two terms of Eq.1 will approach 0 and some constant, respectively. Thus the evidence lower bound (ELBO) effectively becomes $\mathcal{L}_{T}$ and

$$ $\lim_{T\rightarrow\infty}\mathcal{L}_{T}=\int_{0}^{1}\frac{\alpha_{t}^{\prime} }{1-\alpha_{t}}\mathbb{E}_{q(\mathbf{x}_{t}|\mathbf{x}_{0})}[\delta_{\bm{x}_{t },\bm{m}}\bm{x}_{0}^{\top}\log f_{\theta}(\bm{x}_{t})]\,dt.$ (6) $$

The full derivation is listed in Appendix A.2. The same form of ELBO which is invariant to noise schedule but related to the signal-to-noise ratio (SNR) is also introduced in Kingma et al. (); Shi et al. (). Following Austin et al. (), we choose the noise schedule $\alpha_{t}=1-t$, then $\frac{-\alpha_{t}^{\prime}}{1-\alpha_{t}}=\frac{1}{t}$.
The previous discussion focused on the single token $\bm{x}_{t}$, and can be applied independently to a text sequence of $N$ tokens $\mathbf{x}_{t}=[\bm{x}_{t}^{1},\bm{x}_{t}^{2}\dots,\bm{x}_{t}^{N}]$. During training, we do not compute integral loss in Eq.6 for efficiency consideration; instead, we sample $t$ for each data point. The final loss at $t$ is

$$ $\mathcal{L}_{t}^{1:N}=\frac{1}{t}\mathbb{E}_{q(\mathbf{x}_{t}|\mathbf{x}_{0})} \left[-\sum_{n=1}^{N}\delta_{\mathbf{x}_{t}^{n},\bm{m}}(\mathbf{x}_{0}^{n})^{ \top}\log f_{\theta}(\mathbf{x}_{t}^{1:N})_{n}\right],$ (7) $$

where $f_{\theta}(\mathbf{x}_{t}^{1:N})_{n}$ denotes the whole input sequence is fed into the transformer model and the $n$-th output token is indexed.

### 3.2 Unifying Language Modeling Objectives

The training objective of autoregressive (AR) language models is the negative log-likelihood of each ground-truth token provided the preceding tokens,

$$ $\mathcal{L}_{AR}^{1:N}=-\sum_{n=1}^{N}(\mathbf{x}_{0}^{n})^{\top}\log f_{ \theta}(\mathbf{x}_{0}^{1:n-1})_{n-1}.$ (8) $$

Comparing Eq.8 against Eq.7, we note that while both take the form of cross-entropy functions, Eq.7 includes an additional reweighting term $\frac{1}{t}$ and an indicator function $\delta_{\mathbf{x}_{t}^{n},\bm{m}}$. They result from the definition of discrete diffusion processes (§3.1). The reweighting emphasizes smaller $t$ where $\mathbf{x}_{t}$ contains fewer masked tokens, and this can be regarded as the importance sampling (Nichol & Dhariwal, ). The indicator specifies which tokens are masked for prediction. The AR training objective Eq.8, on the other hand, constrains the context to be unidirectional via attention masking and shifts the targets so that each token predicts the next token instead of itself. These discrepancies form the basis of our adaptation framework, which is detailed in §3.3.

In fact, an alternative way to understand AR modeling, through the lens of diffusion models, is to consider a diffusion process where the forward pass deterministically masks right-to-left and token-by-token (Austin et al., ; Hoogeboom et al., ). This yields a backward process generating one token at a time from left to right, running with $T=N$ denoising steps in total. As discussed in Austin et al. (), the loss objective of this diffusion process is equivalent to standard cross-entropy (Eq.8) commonly used to train AR language models. This crafted diffusion process for AR models represents a special case of discrete diffusion (§3.1), yet it is limited to unidirectional context and sequential token generation. In contrast, general discrete diffusion processes can leverage bidirectional context and support parallel generation in arbitrary orders.

### 3.3 Adaptation

Building on the connection between AR modeling and discrete diffusion processes, we construct an adaptation recipe next.
Figure 1 shows an overview of our adaptation approach.
We use attention mask annealing, shift operations, and a time-embedding free architecture to narrow the differences between AR and DLMs.

Figure: Algorithm 1 Adaptation Training

##### Attention Mask Annealing

The prediction of the $n$-th token, given all preceding tokens, $f_{\theta}(\mathbf{x}_{0}^{1:n-1})$, is usually implemented by causal attention masking in transformer-based AR language models.
As shown in Figure 1, causal attention masks set all entries in the upper triangle of the self-attention matrices to zero,
so each token cannot attend to its respective future tokens.
Such causal masking prevents the model from learning right-to-left dependencies for more general diffusion processes.
To address this limitation while preserving left-to-right conditionals during adaptation, we introduce an incremental annealing process from causal masks to full attention matrices.
During annealing, the causal mask is not immediately removed; instead, it is retained at a controlled ratio, as shown in the middle part of Figure 1.
At each training step, we sample the amount of context from the right side and progressively increase this amount till we obtain the full attention mask.

##### Shift Operation

AR models also apply a shifting operation, where the target output is the input sequence shifted left by one position. In other words, the prediction target of the $(n\!-\!1)$-th token is the $n$-th token, contrasting with typical diffusion models that try to predict masked tokens at their original positions. When initializing text diffusion models with AR model parameters, the model would tend to output the hidden representations of the shifted input sequence. If we continue to optimize the cross-entropy objective based on the original token positions, the model struggles to adapt due to misalignment between input and output. Instead, we maintain the shift operation (Algo.1, line 9), treating the output logits at each position as corresponding to the next token. When calculating the objective, we align prediction targets so that the diffusion model learns to recover the original signals. This process is illustrated in the right panel of Figure 1.

##### Time-Embedding-Free Architecture

Many diffusion models for text generation (Li et al., ; Dieleman et al., ; Gulrajani & Hashimoto, ; Lou et al., ; Shi et al., ) incorporate time embedding layers to represent the information of current timesteps $t$, which can explicitly indicate the noise scale of the input noisy data.
While inferring these timesteps can be challenging for image diffusion models (Ho et al., ; Li et al., ), some discrete text diffusion models (He et al., ) assert that timesteps $t$ can be easily learned implicitly based on the number of mask tokens.
Since AR models are not equipped with time embedding layers, we also choose not to use the time embedding, resulting in no additional parameters compared to previous diffusion models.

### 3.4 Sampling

Following Shi et al. (), we initialize $\bm{x}_{T}$ with all [MASK] tokens and then sample tokens according to the time reversal $q(\bm{x}_{s}|\bm{x}_{t},\bm{x}_{0})$ in Eq.4. At each timestep, if $\bm{x}_{t}$ is a mask, it will jump to the predicted $\bm{x}_{0}$ at time $s$ with probability $\frac{\alpha_{s}-\alpha_{t}}{1-\alpha_{t}}$. After $T$ iterations, the model generates the full sequence. Since our adapted models are trained with the shift operation, at each sampling iteration, we shift back the generated sentence and prepend a start token before the next forward pass (Algo.2, line 10). Usually larger $T$ requires more interactions of computation, and can yield texts in higher quality, and this trade-off can be controlled easily through $T$. Through experiments, we find that the output generated by diffusion models is diverse and scattered. Therefore, for conditional generation tasks, we improve the sampling procedure to ensure that only tokens with
high probabilities from neural networks are
denoised (Ghazvininejad et al., ; Chang et al., ; Zheng et al., ), so that the model could predict tokens mostly relevant to the input. In addition, existing sampling techniques for AR language models, including top-$k$ and nucleus sampling (Holtzman et al., ), can be seamlessly applied to diffusion models as well.

## 4 Experiment

### 4.1 Adaptation setup

DiffuGPT We use the 30 billion tokens(^2^22This is the total number of tokens used; however, our effective training tokens exceed this count, meaning that we train for more than one epoch.) random split from the FineWeb dataset (Penedo et al., ), an improved corpus than OpenWebText (Gokaslan & Cohen, ) used in prior DLMs (Lou et al., ), to continue training GPT2 base (Radford et al., ). We use sequence packing, logits shifting, and $10$K-step attention mask annealing to transform GPT2 to DiffuGPT.

Figure: Figure 2: Training loss over tokens for different scales of our adapted diffusion models.
Refer to caption: x2.png

DiffuLLaMA We continue pre-training llama-2-7-hf (Touvron et al., ) on a mixture of SlimPajama (70%) (Soboleva et al., ) and Starcoder (30%) (Li et al., ) data following TinyLLaMA (Zhang et al., ).
We randomly sample 65 billion tokens from this mixture and use sequence packing with context length of $2048$.
For efficient implementation we enable flash-attention 2 (Dao, ) and directly use bi-directional attention without attention mask annealing.

For both adaptation settings, we employ full parameter finetuning with bf16. Please refer to Appendix 6 for details.
We plot the training loss curve in Figure 2. We train DiffuLLaMA on 60B tokens and achieve a lower loss compared to 127M and 335M models, suggesting a scaling trend similar to that of AR LLMs (Kaplan et al., ).
We also note that there is still scope for training more, since the model does not show signs of saturation.

### 4.2 Evaluation setup

Previously developed diffusion language models (Gulrajani & Hashimoto, ; Lou et al., ; Shi et al., ; Ou et al., ) evaluate model performance using zero-shot perplexity on benchmark datasets. However, this metric alone does not fully capture a model’s capabilities for several reasons. First, lower perplexity does not always correlate with human-like content, even in autoregressive models (Kuribayashi et al., ). Additionally, the loss from text diffusion models only indicates an upper bound on negative log-likelihood. While Kingma et al. (); Shi et al. () demonstrate that the ELBO is invariant to the noise scheduler, discrepancies between continuous diffusion, discrete diffusion, and autoregressive loss still hinder fair comparisons across different model types. Given the ample evaluation benchmarks (Gu et al., ) for LLMs, we propose a more comprehensive evaluation for diffusion models.

**Table 1: Comprehensive evaluation of different diffusion language models and the same scale pre-trained autoregressive models. There are 3 types of these models: AR for autoregressive, DD for discrete diffusion and CD for continuous diffusion. For the infilling task, we use ROUGE-1/2/L score; for other tasks, we use the accuracy (%) metric. ^∗ indicates we finetune GSM8K on models; other tasks are all in zero-shot setting. Numbers in the () indicate that AR models are only given prefix for infilling tasks. We bold the best performance among diffusion language models and underline results that surpass their base models.**
| Model | Size | Type | QA | Word | CommonSense Reasoning | Math | Infilling |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| TriQA | Lamb. | HSwag | Wino. | SIQA | PIQA | GSM8K^∗ | ROCStories | Code |  |  |  |
| GPT2-S | 127M | AR | 4.0 | 25.9 | 29.9 | 48.5 | 35.7 | 62.1 | 44.8 | (7.8/0.8/7.4) | (1.6) |
| SEDD-S | 170M | DD | 1.5 | 12.4 | 30.2 | 50.1 | 34.4 | 55.6 | 45.3 | 11.9/0.7/10.9 | 0.7 |
| DiffuGPT-S | 127M | DD | 2.0 | 45.0 | 33.4 | 50.8 | 37.0 | 57.7 | 50.2 | 13.7/1.4/12.6 | 0.3 |
| GPT2-M | 355M | AR | 6.7 | 37.7 | 38.3 | 50.7 | 37.7 | 67.4 | 45.6 | (8.6/0.9/8.2) | (2.6) |
| SEDD-M | 424M | DD | 1.8 | 23.1 | 31.5 | 49.0 | 35.4 | 56.1 | 53.5 | 13.1/1.4/12.2 | 0.5 |
| DiffuGPT-M | 355M | DD | 3.8 | 60.5 | 37.2 | 52.6 | 39.0 | 59.6 | 61.8 | 18.7/2.7/17.0 | 2.9 |
| Plaid1B | 1.3B | CD | 1.2 | 8.6 | 39.3 | 51.3 | 32.3 | 54.5 | 32.6 | 12.1/1.1/11.2 | 0.1 |
| LLaMA2 | 7B | AR | 45.4 | 68.8 | 74.9 | 67.1 | 44.8 | 78.3 | 58.6 | (11.6/2.1/10.5) | (1.7) |
| DiffuLLaMA | 7B | DD | 18.5 | 70.9 | 58.7 | 56.4 | 43.2 | 63.3 | 63.1 | 23.3/5.5/21.2 | 15.5 |

Tasks and Metrics
We consider TriviaQA (Joshi et al., ) to test the reading comprehension of models and last word completion task Lambada (Paperno et al., ) to test how models capture long-range dependencies in text. These two tasks are measured by exact match accuracy.
We also test for common sense reasoning tasks HellaSwag (Zellers et al., ), Winogrande (Sakaguchi et al., ), SIQA (Sap et al., ) and PIQA (Bisk et al., ), all of which involve multiple-choice questions assessed by accuracy. On grade school math problems GSM8K (Cobbe et al., ), we follow Ye et al. () in finetuning setting using the augmented symbolic data to test the CoT (Wei et al., ) math reasoning abilities of diffusion models. Following Shen et al. (), we also test the story infilling tasks using ROCStories (Mostafazadeh et al., ) and evaluate using ROUGE score (Lin, ). To test the code infilling, we adopt Humaneval (Bavarian et al., ) single line infilling task, which is evaluated by pass@1 rate.
We evaluate DiffuLLaMA’s math reasoning and in-context learning ability by evaluating on MAWPS (Koncel-Kedziorski et al., )
and SATMATH
(Zhong et al., ).
We
re-implement all tasks to ensure a fair comparison.

Implementation Details For pre-trained diffusion language models, we mainly use continuous diffusion (CD) model Plaid 1B
(Gulrajani & Hashimoto, ), discrete diffusion (DD) model SEDD
(Lou et al., ) with different scales as baselines.
For autoregressive (AR) baselines, we consider the base models from which our models adapt. We implement infilling tasks for AR models by feeding the prefix and cutting off the generation length using the oracle length, considering that these AR models are not supporting infilling. For the sentence completion task, $T$ is the exact number of ground truth tokens for DD and $32$ for CD. For 4 multi-choices tasks from commonsense reasoning, we compute the loss (Eq.6) of each choice (averaged by token) and choose the one with lowest loss (perplexity). For GSM8K finetuning, we use parameter-efficient LoRA tuning (Hu et al., ) for DiffuLLaMA. The decoding $T$ are set to $32$ by default. The detailed settings are in Appendix B.3.

### 4.3 Language modeling capacities

##### Benchmark performance

According to Table 1, the results on diverse tasks demonstrate that our adapted diffusion models achieve the state-of-the-art results among all existing diffusion language models (DLMs). Notably, by observing different scales of our adapted diffusion models, we can draw the conclusion that scaling diffusion language models results in improved performance. When comparing with their respective AR counterparts, both DiffuGPTs outperform the GPT2 on most tasks. DiffuLLaMA’s performance still falls short of the LLaMA2 model. This discrepancy is presumably attributed to the extensive amount of training tokens processed by the DiffuGPT series models, whereas the 7B model has not undergone equivalent training. TriviaQA and PIQA are significant challenging for DLMs, probably because they require specific physical knowledge, such as the capital of a city or the boiling point of water; while our models are trained on 30B-70B tokens, which may be insufficient to preserve the general knowledge in the original LMs (Ke et al., ).

In tasks that require more extensive global reasoning, such as complex mathematics and coding, DLMs consistently exhibit better performance compared to AR models that rely solely on left-to-right modeling capabilities.
Remarkably, DLMs demonstrate their strengths in infilling tasks.
Regular LLMs like LLaMA2 are not trained for filling-in-the-middle (FIM) tasks like those in  Roziere et al. (), making them incapable of handling infilling. Considering this, we do not provide the suffix information to the model, which might result in an unfair comparison. But the FIM requires re-arranging the order of pre-training/inference sequence with special tokens (Zheng et al., ), while diffusion training naturally supports this in its objective modeling.

Tasks in Table 1 mainly measure conditional modeling abilities, where Plaid 1B performs unsatisfactorily for conditional generation tasks even though with 1B parameters.
We attribute this result to the gap between the continuous diffusion modeling and discrete text representation; in contrast, discrete diffusion models align more closely with AR modeling, naturally supporting conditional generation. Despite this, as illustrated in Figure 3, Plaid 1B demonstrates its strength in unconditional generation, highlighting its language modeling capabilities as a generative model. These findings reveal that the previous evaluation based on the perplexity of test data is too general to accurately assess the model’s true capabilities, while our evaluation offers a more nuanced benchmark.

##### Unconditional Generation

Figure: Figure 3: Quality evaluation for unconditional generation, with perplexity measured by GPT2 large and distinct 2-gram diversity.
Refer to caption: x3.png

We evaluate the quality of text unconditionally generated by DLMs in Figure 3. The perplexity is measured using GPT2 large, consistent with the prior work (Lou et al., ), where the data of MD4 (Shi et al., ) is sourced from its original paper. To make sure low perplexity is not brought by repeated content, we assess the distinct 2-gram diversity of the generated text. Our model achieves low perplexity while maintaining a high level of diversity, validating that the DiffuGPT series excels in fluent text generation.
As the number of decoding steps increases, thereby extending the test computing time, the fluency of unconditional generation improves. Similarly, scaling model size also contribute to better performance. An increase in generation perplexity is often associated with a slight decrease in diversity, which is a common phenomenon. Notably, DiffuGPT outperforms both SEDD and MD4 models, particularly at lower step counts (e.g., 64 steps), while as the continuous diffusion models, Plaid 1B needs more decoding steps to generate more fluent texts. DiffuGPT thus exhibits a significant advantage on less sampling time. We outline the decoding hyperparameters and show the diversity changes across different settings in Appendix C.1, which also includes generation cases.

### 4.4 Analysis on DiffuLLaMA

**Table 2: Performance on math/QA benchmarks ($\uparrow$). We compare of DiffuLLaMA with zero-shot (ZS), few-shot (FS), self-consistency (SC), hit@$k$ and chain-of-thought (CoT) prompts.**
| Models | MAWPS | SATMath | TriviaQA |
| --- | --- | --- | --- |
| LLaMA2 | 63.5 | 24.5 | 45.4 |
| DiffuLLaMA-ZS | 9.7 | $<$1 | 18.5 |
| DiffuLLaMA-FS | 31.3 | 23.6 | 20.9 |
| DiffuLLaMA-SC | 33.1 | 27.7 | 26.0 |
| DiffuLLaMA-@$k$ | 40.8 | 57.7 | 34.1 |
| DiffuLLaMA-CoT | 28.7 | 9.5 | - |

We validate that scaling of DLMs significantly enhances the performance of downstream tasks in Table 1.
Further, we aim to assess if the scaled 7B model demonstrates in-context learning and reasoning capabilities
similar to AR LLMs. Table 2 presents the exact match accuracy between gold labels and predictions generated by DiffuLLaMA across zero-shot (ZS), few-shot (FS), and FS with chain-of-thought (CoT) scenarios. Besides, we deploy the self-consistency approach (Wang et al., ), considering that small DLMs can indeed benefit from this technique (Ye et al., ). We use majority vote to choose the best answer from $3$ individual predictions, and also report the hit rate @$k$ with $k=3$, which counts if any of the predictions hit the correct answer.
For in-context learning (ICL) evaluations, we give $4$-shot on math tasks and $2$-shot on TriviaQA.

The performance improvement from zero-shot to few-shot settings suggests that DiffuLLaMA can learn from ICL examples, particularly in following to the format of answers as we observe. We hypothesize that the adapted model retains some of the abilities from the base AR model.
We randomly select the ICL demonstration here and anticipate that advanced ICL strategies in LLMs (Wu et al., ) could yield potentially higher results.
The self-consistency offers LMs with an effective approach to test-time scaling (Snell et al., ), and DiffuLLaMA shows that it can also leverage this method. Furthermore, we report the hit rate results in generated candidate answers, highlighting the model’s potential to produce the correct answer. This reveals that the current model exhibits high uncertainty about its responses, leading to temporarily suboptimal performance.
We also observe that adding step-wise solutions in the in-context example (CoT) leads to a drop in performance, likely due to the absence of instruction tuning, similar to the findings in LLMs (Ouyang et al., ). We will leave instruction tuning as the future work as Ye et al. () show that text diffusion model can benefit from instruction tuning.
In summary, we show the potential capabilities of DiffuLLaMA, which motivates us to further investigate the scaling of diffusion models.

### 4.5 Discussions

##### Ablation Test on GSM8K-symbolic

**Table 3: Ablation test for adaptation approaches on GSM8K symbolic dataset. CD is for continuous diffusion and DD is for discrete diffusion.**
| Base models | Random | GPT2-S | GPT2-M |
| --- | --- | --- | --- |
| Autoregressive | 30.5 | 44.8 | 45.6 |
| CD | 27.9 | 19.2 | 20.2 |
| DD-w/o shift | - | 33.5 | 34.5 |
| DD-w/o anneal | - | 43.3 | 47.2 |
| DD | 28.0 | 45.4 | 49.7 |

Direct ablation on adaptation training is costly; hence, we conduct preliminary experiments to determine the adaptation recipes.
Following Ye et al. (), we finetune models on the augmented GSM8K symbolic dataset using various base models and training objectives. The models are either trained from scratch (random initialization) or initialized with GPT2-S/M weights. Training objectives includes autoregressive training with a causal mask, continuous diffusion loss (CD), and discrete diffusion loss (DD).
As shown in Table 3, different training objectives yield comparable results when training from scratch.
However, when using GPT2 as the base model, the CD loss performs worse than both the DD and AR losses. We attribute this to the better alignment of DD and AR losses as discussed in §3.2.
Previous continuous diffusion models (Dieleman et al., ; Gulrajani & Hashimoto, ) has reparameterized the estimation of embeddings into the CE loss. However, adapting diffusion models from an AR model in continuous space necessitates an additional projection from the embedding to a categorical distribution, increasing the difficulty of adaptation.

For DD loss, removing attention mask annealing and shift operations both degrade performance, indicating the efficacy of our approaches. The mask annealing has minimal impact, so we choose to omit it for 7B adaptation to simplify implementation using flash-attention 2.

Direct DD loss finetuning on GPT2 achieves accuracy of $45.4$ and $49.7$ for small and medium models, respectively, outperforming GPT2 AR finetuning. However, finetuning from already adapted diffusion language models (DiffuGPT) yields accuracy of $50.2$ and $61.8$ (Table 1). This demonstrates the superiority of DiffuGPT as the current best diffusion base model at this scale and highlights that a better base model leads to improved results. Even with the same DD loss, DiffuGPT’s finetuning converges faster and achieves lower loss, as shown in Appendix C.2.

##### Inference Speed

Figure: Figure 4: Single batch decoding speed (seconds) for different models using flash-attention 2.
Refer to caption: x4.png

AR models usually utilize key-value caching (incremental decoding; Ott et al. ) to enhance throughput during decoding. However, due to the nature of sequential token generation, they are highly memory-bound and cannot fully exploit modern accelerators (Chen et al., ). In contrast, diffusion models, despite not having a concept of caching and requiring self-attention over the entire sequence at each iteration, can operate with fewer iterations than the sequence length and exhibit less memory-bound behavior. Their performance can be further boosted with hardware-aware optimizations like flash-attention (Dao et al., ; Dao, ; Shah et al., ). In Figure 4, we evaluate the decoding latency with batch size 1 using flash-attention 2 and illustrate that our DiffuLLaMA achieves better inference efficiency using $T=256$ when generating sequences of length $1024$ or longer. This underscores the significant potential of diffusion models for efficient inference. Further decreasing $T$ can lead to faster decoding but may sacrifice quality. Additional analysis and latency comparisons are provided in Appendix C.3.

## 5 Related Work

Continue Pre-training
Continue pre-training is commonly used in adapting an existing language model (LM) to a domain-specific LM (Ke et al., ) or enabling new abilities of LM, such as for longer context (Chen et al., ) or code generation (Xu et al., ). Pre-training LMs is non-trivial and expensive (Samragh et al., ), thus in exploring of new architectures of LMs such as Mamba (Gu & Dao, ) and gated attention, Wang et al. (); Zhang et al. () choose to transfer from LMs to save the training cost. However, all these continue pre-training works follow the autoregressive (AR) language modeling, while adapting LMs into diffusion language model is more challenging due to discrepancies between their modeling objectives.

Text Diffusion Models
Diffusion models have demonstrated significant diversity and controllability in image generation (Ho et al., ; Song et al., ; Ramesh et al., ). Building on this success, line of research (Li et al., ; Gong et al., ; ; Dieleman et al., ) build continuous diffusion models for text generation tasks. Among them, Lin et al. () experiment with a pre-training and finetuning framework under a small scale; Gulrajani & Hashimoto () highlight the scaling law of continuous diffusion models, revealing that the compute-optimal requires longer training than their AR counterparts. To address the discrete nature of text, Austin et al. (); Hoogeboom et al. (); Zheng et al. () incorporate an absorbing [MASK] state as noise, laying the foundation for discrete diffusion models, which are further developed by Lou et al. (); Shi et al. (); Ou et al. (); Zhao et al. ().
By connecting text diffusion models with pre-trained masked language models (MLMs; Devlin et al. ), Ye et al. (); He et al. () initialize discrete diffusion models using MLMs. Besides, the unification between diffusion and AR generation is also discussed in image generation (Li et al., ). However, the adaptation of diffusion models from AR LLMs remains unexplored.

Non-autoregressive Generation
Non-autoregressive (NAR) models, introduced by Gu et al. (), break free from the left-to-right generation constraint, allowing for new capabilities like planning with future tokens (Wu et al., ). Current diffusion language models are a notable part of the NAR family (Gong et al., ). Given the challenges of developing NAR models, researchers often seek to find a trade-off. For instance, SSD-LM (Han et al., ) leverages diffusion models to iteratively generate text blocks, facilitating a semi-NAR generation process. Similarly, CLLM (Kou et al., ) enhances LLMs by enabling the parallel generation of $n$ tokens, thereby improving decoding speed. FiLM (Shen et al., ) adapts language models to generate tokens in any order, which is particularly useful for infilling tasks. Additionally, Gloeckle et al. () focus on training models to achieve better and faster multi-token predictions as they scale up. These semi-NAR approaches provide compelling alternatives to traditional AR LLMs, yet few have thoroughly explored the scalability of fully-NAR models.

## 6 Conclusion

Building on existing DLMs, we present a recipe for scaling DLMs by continuing training on off-the-shelf autoregressive LLMs.
Our adaptation technique involves using 1) attention mask annealing to enable bidirectional modeling and 2) shift operation to allow similar training dynamics like AR models.
By unifying the language modeling objectives of autoregressive and diffusion models, we scale diffusion models up to 7B parameters.
Through experiments on common sense reasoning, language modeling, math reasoning and code generation, we show that DiffuGPT and DiffuLLaMA have better performance compared to existing DLMs. We find that DiffuLLaMA is capable of following in-context demonstrations to some extent on math problems.
In the future, we aim to instruction tune our DLMs and explore inference time planning methods.
We release DiffuLLaMA and DiffuGPT for further exploration of diffusion models as an alternative language modeling method.

#### Author Contributions

Shansan Gong: Project lead, methodology development, DiffuGPT training and model evaluation, major writing. Shivam Agarwal: Discussion, DiffuLLaMA training, writing. Yizhe Zhang: Discussion, DiffuLLaMA training, writing suggestions. Jiacheng Ye: Initial methodology exploration. Lin Zheng: Discussion, writing. Mukai Li & Chenxin An: Discussion, writing suggestions. Others: Mentorship and supervision.

## Appendix A Objective Derivations

This section provides detailed preliminary and loss derivations of §2 and §3.1 in the main paper.

### A.1 Background of Diffusion Models

We denote $\mathbf{x}_{0}\sim p_{data}(\mathbf{x}_{0})$ as the variable following the data distribution, and $\mathbf{x}_{t}\sim q(\mathbf{x}_{t})$ as the noisy variable of $\mathbf{x}_{0}$ at time $t$, where the maximum time is $T$. The forward process

$$ $q(\mathbf{x}_{1:T}|\mathbf{x}_{0})=\prod_{t=1}^{T}q(\mathbf{x}_{t}|\mathbf{x}_ {t-1})$ (9) $$

corrupts the initial data $\mathbf{x}_{0}$ into a sequence of increasingly noisy variables $\mathbf{x}_{1:T}$. Accordingly, the reverse Markov process models the joint probability as

$$ $p_{\theta}(\mathbf{x}_{0:T})=p_{\theta}(\mathbf{x}_{T})\prod_{t=1}^{T}p_{ \theta}(\mathbf{x}_{t-1}|\mathbf{x}_{t}),$ (10) $$

which gradually denoises $\mathbf{x}_{t}$ to reconstruct the original data $\mathbf{x}_{0}$. Parameters $\theta$ are learned by minimizing the negative log-likelihood of $\mathbf{x}_{0}$, which can be optimized through the variational lower bound (VLB):

$$ $\displaystyle-\log p_{\theta}(\mathbf{x}_{0})$ $\displaystyle\leq\mathbb{E}_{q(\mathbf{x}_{1}|\mathbf{x}_{0})}[-\log p_{\theta }(\mathbf{x}_{0}|\mathbf{x}_{1})]+D_{\mathrm{KL}}(q(\mathbf{x}_{T}|\mathbf{x}_ {0})||p_{\theta}(\mathbf{x}_{T}))+\mathcal{L}_{T},$ (11) $\displaystyle\text{with }\mathcal{L}_{T}$ $\displaystyle=\sum_{t=2}^{T}\mathbb{E}_{q(\mathbf{x}_{t}|\mathbf{x}_{0})}[D_{ \mathrm{KL}}(q(\mathbf{x}_{t-1}|\mathbf{x}_{t},\mathbf{x}_{0})||p_{\theta}( \mathbf{x}_{t-1}|\mathbf{x}_{t}))].$ (12) $$

For continuous text diffusion (Li et al., ; Gong et al., ), at each forward step, perturbations are applied according to

$$ $q(\mathbf{x}_{t}|\mathbf{x}_{t-1})=\mathcal{N}(\mathbf{x}_{t};\sqrt{1-\beta_{t }}\mathbf{x}_{t-1},{\beta}_{t}\mathbf{I}),$ (13) $$

where $\beta_{t}\in(0,1)$ represents different scales. In the end, $\mathbf{x}_{T}\sim\mathcal{N}(0,\mathbf{I})$.
In the case of discrete denoising models (Ho et al., ; Austin et al., ; Zheng et al., ), $\mathbf{x}_{t}$ follows a categorical distribution which naturally aligns with discrete text data. Let $\bm{x}$ be the one-hot encoded sample of variable $\mathbf{x}$ and $\mathbf{x}_{t}\sim\text{Cat}(\bm{x}_{t};\bm{p})$ represent a categorical distribution over vector $\bm{x}$ with probabilities given by $\bm{p}$. Here, $K$ represents the vocabulary size, $\bm{x}\in\{\bm{e}_{1},\dots,\bm{e}_{K}\}$, and $\bm{e}_{k}\in\{0,1\}^{K}$ is the one-hot encoding of the $k$-th word category. The forward process can be formulated through a transition matrix $\bm{Q}_{t}\in[0,1]^{K\times K}$ such that

$$ $q(\mathbf{x}_{t}|\mathbf{x}_{t-1})=\text{Cat}(\bm{x}_{t};\bm{Q}_{t}^{\top}\bm{ x}_{t-1});\bm{Q}_{t}=(1-\beta_{t})I+\beta_{t}\mathbf{1}\bm{e}_{K}^{\top},$ (14) $$

with $\mathbf{1}$ as an all-one vector of size $K$ and we assume $\bm{e}_{K}$ as the special [mask] state, also defined as the absorbing state in discrete diffusion $\bm{m}$. Each entry in $[\bm{Q}_{t}]_{ij}$ denotes the probability of transition from the state $\bm{e}_{i}$ to $\bm{e}_{j}$, and thus the previously defined $\bm{Q}_{t}$ means with probability $1-\beta_{t}$, $\bm{x}_{t}$ will stay unchanged and otherwise it will jump to the mask state $\bm{e}_{K}$.

Starting from $\bm{x}_{0}$, the $t$-step marginal distribution and the posterior at previous time $t-1$ is respectively

$$ $q(\bm{x}_{t}|\bm{x}_{0})=\text{Cat}(\bm{x}_{t};\bm{p}=\bm{\overline{Q}}_{t}^{ \top}\bm{x}_{0});\;q(\bm{x}_{t-1}|\bm{x}_{t},\bm{x}_{0})=\frac{q(\bm{x}_{t}| \bm{x}_{t-1},\bm{x}_{0})q(\bm{x}_{t-1}|\bm{x}_{0})}{q(\bm{x}_{t}|\bm{x}_{0})}$ (15) $$

where cumulative products $\bm{\overline{Q}}_{t}=\prod_{i=1}^{t}\bm{Q}_{i}=\alpha_{t}I+(1-\alpha_{t})
\mathbf{1}\bm{m}^{\top}$, and $\alpha_{t}=\prod_{i=1}^{t}(1-\beta_{t})$. We expect $\alpha_{T}$ approaches 0 0 such that the full noise data $\bm{x}_{T}$ is equal to $\bm{e}_{K}$ with probability $1$.
In the following sections, we primarily takes the discrete diffusion formulation.

### A.2 Loss Derivation

Previous discrete time $t\in[0,T]$ restricts $\bm{x}_{t}$ to fixed time points whereas the continuous-time sampling allows for more flexibility covering any point in the range (Kingma et al., ; Shi et al., ; Zhao et al., ; Ou et al., ). In this case, $t$ runs from 0 0 to $1$, corresponding to dividing $[0,1]$ into $T$ intervals and let $T\rightarrow\infty$. For any two arbitrary time points, $0\leq s<t\leq 1$, the forward modeling can be generalized from $q(\mathbf{x}_{t}|\mathbf{x}_{t-1})$ to $q(\mathbf{x}_{t}|\mathbf{x}_{s})$. We uniformly adopt the notation of continuous-time in following sections.

Following the previous definition, after simplification, we have $q(\bm{x}_{t}|\bm{x}_{0})=\alpha_{t}\bm{x}_{0}+(1-\alpha_{t})\bm{m}$, referring to the probability of transition to absorbing mask state. Given $q(\bm{x}_{t}|\bm{x}_{0})=q(\bm{x}_{t}|\bm{x}_{s})q(\bm{x}_{s}|\bm{x}_{0})$, we can derive the transition distribution between two arbitrary times $s$ and $t$:

$$ $q(\bm{x}_{t}|\bm{x}_{s})=\text{Cat}(\bm{x}_{t};\bm{\overline{Q}}_{s|t}^{\top} \bm{x}_{s}),\;\text{with }\bm{\overline{Q}}_{s|t}=\bm{\overline{Q}}_{s}^{-1} \bm{\overline{Q}}_{t}=\frac{\alpha_{t}}{\alpha_{s}}I+(1-\frac{\alpha_{t}}{ \alpha_{s}})\mathbf{1}\bm{m}^{\top}.$ (16) $$

Similarly, after simplification,

$$ $q(\bm{x}_{t}|\bm{x}_{s})=\frac{\alpha_{t}}{\alpha_{s}}\bm{x}_{s}+(1-\frac{ \alpha_{t}}{\alpha_{s}})\bm{m}.$ (17) $$

Following Zheng et al. (); Shi et al. () and extend the formulation to continuous time, we have the backward transition probability:

$$ $q(\bm{x}_{s}|\bm{x}_{t},\bm{x}_{0})=\frac{q(\bm{x}_{t}|\bm{x}_{s})q(\bm{x}_{s} |\bm{x}_{0})}{q(\bm{x}_{t}|\bm{x}_{0})}=\begin{cases}\frac{1\cdot(1-\alpha_{s} )}{1-\alpha_{t}}=\frac{1-\alpha_{s}}{1-\alpha_{t}}=1-\frac{\alpha_{s}-\alpha_{ t}}{1-\alpha_{t}}&\text{if }\bm{x}_{t}=\bm{x}_{s}=\bm{m},\\ \frac{(1-\frac{\alpha_{t}}{\alpha_{s}})\cdot\alpha_{s}}{1-\alpha_{t}}=\frac{ \alpha_{s}-\alpha_{t}}{1-\alpha_{t}}&\text{if }\bm{x}_{t}=\bm{m}\neq\bm{x}_{s} .\\ \end{cases}$ (18) $$

For $\bm{x}_{t}\neq\bm{m}$, the $q(\bm{x}_{s}|\bm{x}_{t},\bm{x}_{0})$ will stick to the observed data. For $\bm{x}_{t}=\bm{m}$, we get the simplified

$$ $q(\bm{x}_{s}|\bm{x}_{t},\bm{x}_{0})=\frac{\alpha_{s}-\alpha_{t}}{1-\alpha_{t}} \bm{x}_{0}+\frac{1-\alpha_{s}}{1-\alpha_{t}}\bm{m}.$ (19) $$

In diffusion process, the generative model aims to approximate the reverse transitions using a denoising model $p_{\theta}(\bm{x_{s}}|\bm{x}_{t},f_{\theta}(\bm{x}_{t}))\rightsquigarrow q(\bm
{x}_{s}|\bm{x}_{t},\bm{x}_{0})$, where $f_{\theta}(\bm{x}_{t})$ represents the probability vector obtained from the softmax applied to the logits generated by the neural network, usually using transformer networks (Vaswani et al., ) in text domain. We can similarly have

$$ $p_{\theta}(\bm{x_{s}}|\bm{x}_{t})=\frac{\alpha_{s}-\alpha_{t}}{1-\alpha_{t}}f_ {\theta}(\bm{x}_{t})+\frac{1-\alpha_{s}}{1-\alpha_{t}}\bm{m}.$ (20) $$

Given Eq.19 and Eq.20, the KL-divergence loss is optimized by

$$ $D_{\mathrm{KL}}(q(\bm{x}_{s}|\bm{x}_{t},\bm{x}_{0})||p_{\theta}(\bm{x}_{s}|| \bm{x}_{t}))=\begin{cases}\frac{\alpha_{s}-\alpha_{t}}{1-\alpha_{t}}D_{\mathrm {KL}}(\bm{x}_{0}||f_{\theta}(\bm{x}_{t})),&\text{for }\bm{x}_{t}=\bm{m};\\ 0,&\text{for }\bm{x}_{t}\neq\bm{m}.\\ \end{cases}$ (21) $$

We can use the indicator function $\delta_{\bm{x}_{t},\bm{m}}$ to unify the conditional cases. In addition, given $\bm{x}_{0}$, we have $D_{\mathrm{KL}}(\bm{x}_{0}||f_{\theta}(\bm{x}_{t}))=-\bm{x}_{0}^{\top}\log f_{
\theta}(\bm{x}_{t})$ which corresponds to the cross-entropy widely used in the classification. Therefore, we have

$$ $D_{\mathrm{KL}}(q(\bm{x}_{s}|\bm{x}_{t},\bm{x}_{0})||p_{\theta}(\bm{x}_{s}|| \bm{x}_{t}))=-\frac{\alpha_{s}-\alpha_{t}}{1-\alpha_{t}}\delta_{\bm{x}_{t},\bm {m}}\bm{x}_{0}^{\top}\log f_{\theta}(\bm{x}_{t}).$ (22) $$

Following Eq.12, if we set a small timestep $\Delta_{t}=t-s=\frac{1}{T}\in(0,1)$,

$$ $\mathcal{L}_{T}=\sum_{t=2}^{T}[-\frac{\alpha_{s}-\alpha_{t}}{(t-s)(1-\alpha_{t })}\delta_{\bm{x}_{t},\bm{m}}\bm{x}_{0}^{\top}\log f_{\theta}(\bm{x}_{t}) \Delta_{t}].$ (23) $$

By taking the limit as $T\rightarrow\infty$, we have $\alpha_{t}^{\prime}=\frac{\alpha_{t}-\alpha_{s}}{t-s}$, and the sum is transformed into an integral:

$$ $\lim_{T\rightarrow\infty}\mathcal{L}_{T}=\int_{0}^{1}\frac{\alpha_{t}^{\prime} }{1-\alpha_{t}}\mathbb{E}_{q(\mathbf{x}_{t}|\mathbf{x}_{0})}[\delta_{\bm{x}_{t },\bm{m}}\bm{x}_{0}^{\top}\log f_{\theta}(\bm{x}_{t})]\,dt.$ (24) $$

Also, the first two terms in Eq.11 are $\rightarrow 0$ and a constant, respectively. Thus we can formulate the evidence lower bound (ELBO) of $-\log p_{\theta}(\mathbf{x}_{0})$ as Eq.24.

The same form of ELBO which is invariant to noise schedule but related to the signal-to-noise ratio (SNR) is also introduced in Kingma et al. (); Shi et al. (). Following Austin et al. (); Zheng et al. (), we choose the noise schedule $\alpha_{t}=1-t$, then $\frac{-\alpha_{t}^{\prime}}{1-\alpha_{t}}=\frac{1}{t}$.

The previous discussion focused on the single token $\bm{x}_{t}$, and can be easily extended to a text sequence of length $N$ represented as $\mathbf{x}_{t}=[\bm{x}_{t}^{1},\bm{x}_{t}^{2}\dots,\bm{x}_{t}^{N}]$. The final loss of the whole sequence is

$$ $\mathcal{L}_{t}^{1:N}=\frac{1}{t}\mathbb{E}_{q(\mathbf{x}_{t}|\mathbf{x}_{0})} \left[-\sum_{n=1}^{N}\delta_{\mathbf{x}_{t}^{n},\bm{m}}(\mathbf{x}_{0}^{n})^{ \top}\log f_{\theta}(\mathbf{x}_{t}^{1:N})_{n}\right],$ (25) $$

where $f_{\theta}(\mathbf{x}_{t}^{1:N})_{n}$ denotes the whole input sequence is fed into the transformer model and the $n$-th output token is indexed. During training, we sample $t$ for each data point to optimize the expectation in $\mathcal{L}_{t}^{1:N}$ instead of the integral $\mathcal{L}_{T}$, while for evaluation, we use integral $\mathcal{L}_{T}$.

## Appendix B Implementation Details

### B.1 Training data

##### DiffuGPT

Previous diffusion language models such as Plaid 1B (Gulrajani & Hashimoto, ), SEDD (Lou et al., ) and MD4 (Shi et al., ) use OpenWebText (Gokaslan & Cohen, ) to pre-train from scratch, referring to GPT2 (Radford et al., ). We choose the advanced FineWeb(^3^33[https://huggingface.co/datasets/HuggingFaceFW/fineweb](https://huggingface.co/datasets/HuggingFaceFW/fineweb)) corpus (Penedo et al., ), which is also derived from Common Crawl. We randomly sample 30 billion tokens from subset sample-100BT.

##### DiffuLLaMA

Following Zhang et al. ()(^4^44[https://github.com/jzhang38/TinyLlama](https://github.com/jzhang38/TinyLlama)) we construct the training data for DiffuLLaMA by mixing SlimPajama (Soboleva et al., ) and Starcoder data (Li et al., ).
We randomly sample 65 billion tokens in the ratio of 7:3 from SlimPajama and Starcoder, respectively.
We use sequence packing and pre-tokenize the dataset for efficient computing.

### B.2 Model optimization and hyperparameters

##### DiffuGPT

We implement DiffuGPT using LLaMA-Factory(^5^55[https://github.com/hiyouga/LLaMA-Factory](https://github.com/hiyouga/LLaMA-Factory)) with DeepSpeed Zero-2 parallelization (Rajbhandari et al., ). The hyperparameter setting compared with previous work is listed in Table 4. The global batch size is calculated by multiplying the single GPU batch size, the number of gradient accumulation steps, and the number of GPUs, where we use 8 A100 80G. We use learning rate of $3e-4$ with cosine scheduler. The warm up steps are set to 2K and attention mask annealing steps are 10K. As shown in Table 4, our effective training tokens are less or equal than SEDD and MD4, while DiffuGPT exhibits better performance according to Table 1 and Figure 3.

**Table 4: Training settings for different diffusion language models.**
| Models | Training steps | Global batch size | Context length |
| --- | --- | --- | --- |
| SEDD (Lou et al., ) | 400k | 512 | 1024 |
| MD4 (Shi et al., ) | 1000k | 512 | 1024 |
| DiffuGPT-S | 1000k | 256 | 512 |
| DiffuGPT-M | 160k | 1280 | 1024 |

##### DiffuLLaMA

For a more efficient pre-training, we implement DiffuLLaMA using huggingface(^6^66[https://github.com/huggingface/transformers](https://github.com/huggingface/transformers)).
We use DeepSpeed Zero-3 parallelization with CPU offloading (Rajbhandari et al., ) to efficiently scale DiffuLLaMA to multiple GPUs and nodes.
Furthermore, we use flash-attention 2 and fused cross-entropy loss for optimized GPU memory usage and compute time (Dao, ).
With these settings, we get set a batch size of 60 per GPU with context length 2048 on a GH200 96GB GPU.
We use AdamW (Loshchilov & Hutter, ) to optimize our models with a constant learning rate of $2e-5$ and accumulate gradients every $4$ steps.
We train our model for 65 billion tokens on $16$ 4xGH200 nodes.

##### Tokenizer

During adaptation, we do not change the tokenizer of the base model. In theory, we should expand the original vocabulary by adding an additional dimension to include a special token as [MASK] token. However, considering practical issues on implementation, we can alternatively select an existing word from the vocabulary to serve as the [MASK] token. It is preferable that this chosen word has a particularly low frequency of occurrence in corpus. For DiffuGPT-S we use tokenid=10541 and for DiffuGPT-M we set a new [MASK] token with tokenid=50257. For DiffuLLaMA, we set tokenid=811.

### B.3 Evaluation Details

##### Generation tasks

For the TriviaQA and Lambada sentence completion tasks, we generate $n$-tokens for continue-writing. In triviaQA, we set $n$ to the oracle length plus an additional $10$ tokens, and we only evaluate the first 2000 cases in this dataset for efficiency. For Lambada, which requires the completion of the last word, we set $n$ to oracle length of that word’s tokens, which might be larger than $1$ based on the tokenizer. For DLMs, we set the diffusion timesteps $T$ to the required generation length. For AR baselines, we cut off maximum new tokens. For SATMATH and MAWPS, we integrate our model into math-evaluation-harness(^7^77[https://github.com/ZubinGou/math-evaluation-harness](https://github.com/ZubinGou/math-evaluation-harness)).

##### CommonSense Reasoning tasks

The 4 commonSense reasoning tasks are multiple-choices questions with 4 options. Instead of open generation, we calculate the diffusion loss for each Question+choice pair using Eq.25. A lower loss (perplexity) indicates the model thinks that choice most suitable. This approach is commonly employed in ICL of LLMs (Wu et al., ). We also use this for AR baselines.

##### Finetune GSM8K-symbolic

The setting of finetune GSM8K-symbolic dataset is following Ye et al. ()(^8^88[https://github.com/HKUNLP/diffusion-of-thoughts](https://github.com/HKUNLP/diffusion-of-thoughts)), which enables the diffusion model to perform chain-of-thought reasoning. For DiffuLLaMA, we use parameter-efficient-finetune: LoRA Tuning (Hu et al., ). We set rank to 8 and enable the finetuning of the word embedding layer, with 151 million (2%) parameters involved. For this task, we use $T=64$ for the decoding of DLMs.

##### Infilling tasks

For ROCstories, where each case is a $5$-sentence story, we setup evaluation referring Shen et al. ().The model is tasked with infilling the third sentence based on the first two and last two sentences. We evaluate the first 1000 cases in this dataset for efficiency.
For code infilling, we use humaneval-single-line infilling
(^9^99[https://github.com/openai/human-eval-infilling](https://github.com/openai/human-eval-infilling)) and their evaluation toolkit, which contains 1033 test cases. We implement infilling tasks for AR models by feeding the prefix and cutting off the generation length using the oracle length, considering that these AR models are not supporting infilling. We also try to feed the suffix information using the instruction like Given prefix and suffix please infill the middle, however, LLaMA2 can not follow this instruction. For AR LLMs, to perform infilling tasks requires additional FIM training (Roziere et al., ) or carefully instruction tuning.

##### Unconditional Generation

For unconditional generation in Figure 3, we set the temperature of top-$k$ to 0.98 and top-p to 0.9 for the medium-sized model, while using top-$k$ of 1.0 and top-p of 0.9 for the small model. We generate 64 samples and evaluate the perplexity using the GPT-2 large model, aligning with Lou et al. (); Shi et al. ().

## Appendix C Additional Results

### C.1 Unconditional generation

The generation quality is different for different hyperparameters, shown in Figure 5. Lowering the temperature increases fluency but reduces diversity, leading to noticeable repetition in sentences.

Figure: Figure 5: The unconditional generation quality for different diffusion time steps $T$ and sampling algorithms. We annotate the temperature of top-$k$ sampling and top-p sampling.
Refer to caption: x5.png

We randomly selected samples generated by our DiffuGPT-M models with 1024 tokens for various $T$, as shown in Table 6, Table 7, and Table 8. Lower $T$ values result in less fluent text.

### C.2 Ablation on GSM8K-symbolic

Using the same discrete diffusion loss, if we direct finetune on GPT2 achieves accuracy of $45.4$ and $49.7$ for small and medium models, respectively. In contrast, Finetuning from DiffuGPT yields accuracy of $50.2$ and $61.8$ (Table 1). Comparing with GPT2, DiffuGPT, as the base model, converges faster and attains a lower loss, as shown in Figure 6. This indicates that a better base model leads to improved results and also demonstrates the superiority of DiffuGPT as the current best diffusion base model.

Figure: Figure 6: Finetune GSM8K data with discrete diffusion objectives, using a base model of either GPT2-S/M or DiffuGPT-S/M. DiffuGPT converges faster and attains a lower loss.
Refer to caption: x6.png

### C.3 Decoding Speed Testing

We evaluate the inference time of LLaMA2 and DiffuLLaMA for unconditional text generation across various lengths. Our tests include vanilla attention, flash attention 2, and the torch version of flash attention SDPA, as shown in Table 5.

**Table 5: Single batch inference time for different attention implementation and generation lengths.**
| Length | Attention | DiffuLLaMA (sec) | LLaMA (sec) |
| --- | --- | --- | --- |
| 512 | flash-attention 2 | 12.5 | 9.2 |
| 1024 | SDPA | 13.2 | 16.3 |
| 1024 | flash-attention 2 | 13.3 | 17.5 |
| 1024 | vanilla | 16.2 | 17.2 |
| 2048 | SDPA | 28.5 | 29.5 |
| 2048 | flash-attention 2 | 23.5 | 35.7 |
| 2048 | vanilla | 38.1 | 32.8 |

Table: Table 6: Generation examples of DiffuGPT-M ($T=1024)$.

Table: Table 7: Generation examples of DiffuGPT-M ($T=256)$.

Table: Table 8: Generation examples of DiffuGPT-M in 1024 tokens ($T=32)$.

## Peer Reviews

confidence: 4
contribution: 2
initial_rating: 5
presentation: 3
questions: See weaknesses.
soundness: 3
strengths: The paper presents a simple and effective approach to adapting AR models to build DLMs, bridging the gap between the two modeling paradigms, while the proposed continual discrete diffusion pre-training approach for training diffusion models is practical and effective.
The proposed models, DiffuGPT and DiffuLLaMA, show competitive performance with AR models and outperform earlier DLMs in generating fluent text, perform in-context learning, filling in the middle without prompt re-ordering, and following instructions. 
The writing, organization and presentation of the paper are also good; I enjoyed reading the manuscript.
summary: The paper studies diffusion language models (DLMs) and how they could be a good alternative to autoregressive (AR) LMs for generating text. It highlights the lack of fair comparisons on language modeling benchmarks and the challenges of training DLMs at scale. The authors propose adapting open-source AR models to build text diffusion models. By demonstrating the connections between AR and diffusion modeling objectives, they introduce a simple continual pre-training approach for training these models. The study shows that popular AR LMs can be converted into diffusion models (DiffuGPT and DiffuLLaMA) using less than 200B tokens for training, outperforming earlier DLMs and being competitive with their AR counterparts. The paper contributes a suite of DLMs capable of generating fluent text, performing in-context learning, text in-filling and following instructions.
weaknesses: Overall, I appreciate the achievement of well-performing (discrete) diffusion LMs at scale, but I do have some concerns regarding novelty and evaluation. 

**About building DLMs by scaling and adapting from pre-trained large-scale LMs:**
Building (discrete) diffusion LMs from pre-trained Masked LMs has been studied in [1], while scaling and instruct-tuning (discrete) diffusion by adapting large-scale pre-trained LMs (mainly Masked-LMs while they also attempted to use AR-LMs/Llama1 to test reasoning) has also been studied in [2]. While this paper makes a solid step forward and effectively improves the performance of DLMs by leveraging AR LLMs, the authors should have thoroughly discussed the connections and major differences of their proposed approach with these prior works in the introduction or at least method/related work sections. Can the authors elorabrate the substantial differences and new contributions introduced by this paper?

**About progressively adapting AR text generation models into non-AR models:**
Two core techniques introduced in this paper are "Attention Mask Annealing" and "Shift Operation" to effectively reprogram an AR LM into a DLM. However, a similar approach has also been proposed in [3] in the case of non-autoregressive machine translation, which should have been discussed in this paper.

**Some claims are not supported by evaluations, hence the true advantages of DLMs are not convincing:**
The paper introduces the motivation of pushing the limits of DLMs by arguing that 
> Notable challenges include difficulties in **future planning** (Bachmann & Nagarajan, 2024; Hu* et al., 2024; Xie et al., 2024) and **self-correction** (Huang et al., 2024). These constraints have spurred researchers to explore alternative architectures for next-generation LLMs.

and accordingly,
> Notably, DLMs exhibit promising capabilities in **intermediate token correction** (Ye et al., 2024) and **global planning** (Zhang et al., 2023), thereby addressing key limitations inherent in the AR approach.

However, there is no clear evidence in this paper, not even qualitative ones or case studies, to showcase that DiffuGPT and DiffuLLaMA possess such promising capabilities of self-correction and global planning. Only evaluating on language understanding benchmarks with weaker performance compared to AR-LLMs (Table 1) cannot convince the community why we need really DLMs as an alternative to AR LMs and as a new LLM paradigm (I think this is the most important question every DLM paper needs to address). Plus, the in-filling performance of AR-LMs was unfairly assessed as they are only provided with prefixes, according to Table 1's caption. Thus, the paper still fails to demonstrate the unique, distinct advantages of DLMs over AR-LMs. I strongly suggest the authors provide more evidence to differentiate DLMs' strengths in these regards, which can also support the motivations of this work in the introduction.

Overall, I think this manuscript stands a good contributions to DLM research, and I believe it could be greatly improved if authors can address the aforementioned concerns. 

----

[1] DiffusionBERT: Improving generative masked language models with diffusion models. ACL 2023

[2]  Diffusion language models can perform many tasks with scaling and instruction-finetuning. Arxiv 2023

[3] Fine-Tuning by Curriculum Learning for Non-Autoregressive Neural Machine Translation. AAAI 2020

---

confidence: 3
contribution: 3
initial_rating: 3
presentation: 4
questions: * From the paper, it is unclear to what extent the continuous-time discrete diffusion processes described in 3.1 are a novel contribution. If this is not novel, I would move it to section 2 for clarity about your contributions.

* In diffusion processes, do we need to know the number of tokens ahead of time in order to know the number of MASK tokens? If not, how is decoding done?
soundness: 2
strengths: * Adapting AR models to diffusion models is a problem that is of interest to the ICLR community.
* The proposed method is intuitive and simple.
* The paper is well written and flows really well.
* The results demonstrate that the adaptation is successful to some extent: Adapting larger LLMs leads to better performance.
* The DD model shows superior performance on some tasks that mostly require infilling.
summary: The paper introduces a methodology for adapting pretrained autoregressive (AR) language models to discrete diffusion (DD) models. It identifies two main points of conflict between them: 1) Causal attention (AR) vs. bidirectional attention (DD), 2) next-token-prediciton (AR) vs. denoising (DD). In order to resolve 1), the paper proposes attention mask annealing, where the causal attention mask is slowly turned into a full attention mask over training. For 2), the DD loss is adapted by shifting the logits by 1 to be in line with AR models.
In the experimental evaluation, they continue to finetune pretrained AR models of various sizes using the derived adaptation scheme. The models are evaluated on various knowledge, reasoning, coding, and math benchmarks.
weaknesses: 1. In lines 364-368, it states that "by observing different scales of our adapted diffusion models, we can draw the conclusion that scaling diffusion language models results in improved performance". This statement suggests that if a DD model was trained from scratch, performance would scale with the size of the model. However, this isn't supported by the experiments, which merely shows that AR models of increasing size can be adapted to DD models in such a way, that larger adapted models perform better than smaller adapted models. However, it is possible that the adaptation process is merely retaining some of the knowledge/skills that were learned by the pretrained AR model. It doesn't mean that the DD model could attain these capabilities itself through scaling. I think it is important to be precise here.

2. In lines 367-369: "This discrepancy [between DiffuGPT's performance compared to the base model vs. DiffuLLaMA's performance compared to the base model] is presumably attributed to the extensive amount of training tokens processed by the DiffuGPT series models, whereas the 7B model has not undergone equivalent training." This explanation may be true, but needs to be verified. Since DiffuLLaMA has been pretrained on more than twice as many tokens (65B vs 30B), it doesn't seem obvious. What is the reason not to finetune both models on the same data?

3. In lines 373-375: "In tasks that require more extensive global reasoning, such as complex mathematics and coding, DLMs consistently exhibit better performance compared to AR models that rely solely on left-to-right modeling capabilities." This claim can only be substantiated through a controlled experiment that continues to finetune the base model on the same data in AR mode vs DD mode. Table 3 conducts this experiment, but only on a single downstream dataset that is quite small. Having a fair, controlled comparison between AR and DD models is the biggest weakness of this paper.

4. Table 2: Different models here correspond to different prompting methods. hit@k is not a prompting method, it is an evaluation metric whose value is at least as high as the standard evaluation metric with hit@1. Stylizing the respective row with hit@k incorrectly suggests that this is the best "method", which could mislead the reader into thinking that the difference to the LLaMA-2 baseline is smaller than it actually is.

---

confidence: 4
contribution: 3
initial_rating: 6
presentation: 3
questions: see weaknesses.
soundness: 3
strengths: 1. The paper proposes to adapt AR pretraining parameters to Diffusion parameters, which solves a very important problem about improving the training efficiency of diffusion models. 
2. The result seems solid, with a fair amount of improvement over previous diffusion models. But I still think there are some unresolved problems as shown in the weakness section. 
3. The experiment seems pretty comprehensive, with a wide range of downstream task, generation quality, analysis, ablation, and inference efficiency.
summary: This paper proposes to adapt pre-trained autoregressive models to build discrete diffusion models via continual pre-training. This way, they can convert AR to diffusion parameters by training on fewer than 200B tokens. Technically, they propose  (1) annealed attention masking, (2) inheriting the shift inductive bias from AR. The experiment section suggests that this diffusion model demonstrates strong performance in math, word lambada, and infilling, and ablation suggests that the shift inductive bias is crucial for the transfer.
weaknesses: Since the paper claimed to tackle the parameter transferability problem, there remain some unresolved scientific questions: 
(1) suppose we have more compute, is this transfer still optimal? would this transfer converge to a worse local optimum than if we train from scratch for longer? 
(2) The paper included ablation results on GSM8K performance, but more fundamentally, what's the loss in terms of PPL for the (without shift) and (without annealing) baselines? I think these are more important and more general-purpose to report than a specific downstream task. I saw the disclaimer that PPL may not directly reflect the correctness and it's only ELBO. I still think it's good to report ELBO on the test set in the paper.   
(3) What's the number of flops for the training? 200B tokens is a bit abstract, especially 200B token for diffusion is different from 200B token for AR (due to lack of KV caching) and 200B token means different Flops across model sizes.

---

confidence: 4
contribution: 3
initial_rating: 8
presentation: 2
questions: The current T is set to 32. It would help to see the quality performance across different T, since it was mentioned in section 4.5 that decreasing T leads to faster decoding but with loss of quality.
Please include this.
soundness: 4
strengths: - Well-written and easy to understand.
- Comprehensive evaluation on multiple tasks, including word completion, reading comprehension, commonsense reasoning, math problems, and coding.
- Ablation study conducted to emphasize the importance of shift operation and attention mask annealing.
- Mathematically grounded and novel approach.
- Demonstrates increased token diversity without compromising quality.
summary: The paper addresses limitations in autoregressive (AR) models, particularly issues with global planning and intermediate token correction. In response, Diffusion Language Models (DLMs) were introduced but face scalability challenges due to the computational costs of training with only 400 billion tokens. This work proposes a novel training mechanism that redefines DLM objectives. The approach also addresses architectural limitations in AR models, using attention mask annealing and a shift operation to remove causal masking bias. Scaled models ranging from 127 million to 7 billion parameters, specifically DiffuGPT and DiffuLLaMA, demonstrate better or comparable performance to existing AR models. Additionally, the authors release open-source code for these models, providing valuable resources to the research community for faster inference speeds with minimal iterations.
weaknesses: - Missing qualitative examples and human evaluation.
- No statistical significance testing across tasks.
- The current T is set to 32. It would help to see the quality performance across different T, since it was mentioned in section 4.5 that decreasing T leads to faster decoding but with loss of quality.

Meta-review: The authors study diffusion language models. In particular, they come up with compute efficient ways of adapting a pre-trained AR model into a diffusion one, and show that these resulting adapted diffusion models are performant and generally comparable to their original AR equivalents.

While adapting an AR model to diffusions is not amazingly novel, the reviewers generally agree that the results are compelling, and of interest to the diffusion language modeling community. The evaluations are also solid enough that these results can be used as foundations for future work, and its likely that these types of techniques will be used to more computationally efficiently study diffusion models.

Decision: Accept (Poster)