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\title{\textbf{ADAPT-DIFF: Adaptive Latent Diffusion with Actor-Critic Branch-and-Bound Tree Search for Token Sampling in Dense LLMs}}
\author{
  \textbf{Nick Cantrell} \\
  ASI Research Lab \\
  \texttt{research@cybergolem.ai}
}
\date{June 2026}

\begin{document}

\maketitle

\begin{abstract}
Autoregressive decoding in large language models (LLMs) creates a memory-bandwidth bottleneck by loading the entire model's parameters from High Bandwidth Memory for each generated token. We present ADAPT-DIFF (Adaptive Latent Diffusion with Actor-Critic Branch-and-Bound Tree Search), which breaks this sequential generation bottleneck. ADAPT-DIFF operates in two stages over a custom bidirectional Qwen backbone. First, 4-bit quantized Latent Diffusion Model (LDM) heads predict continuous latent token embeddings in parallel blocks of size $L$, initializing candidate tokens. Second, a recursive refinement mechanism monitors Logits-Induced Token Uncertainty (LogTokU). High-uncertainty tokens are selectively refined via bfloat16 forward passes. The refinement process is formulated as a Markov Decision Process (MDP) solved via an Actor-Critic Branch-and-Bound tree search with Alpha-Beta pruning. On a single NVIDIA A100 GPU with a Qwen-3.5-0.8B backbone, ADAPT-DIFF achieves a generation throughput of 61 tokens/second (a $\approx$3$\times$ speedup) while reducing relative FLOPs per token by 6$\times$.
\end{abstract}

\section{Introduction}
Autoregressive large language models (LLMs) generate sequences token-by-token, a process limited by the memory bandwidth of loading model weights for each decoding step. While speculative decoding and draft-verification architectures partially mitigate this, they rely on auxiliary draft models that often perform poorly on out-of-distribution reasoning trajectories.

We introduce ADAPT-DIFF (Adaptive Latent Diffusion with Actor-Critic Branch-and-Bound Tree Search), which reframes sequence generation as a hybrid process of parallel continuous initialization followed by localized, precision-routed refinement.

The contributions are:
\begin{itemize}
    \item Parallel Latent Diffusion Initialization: We stack 4-bit quantized LDM heads on the final transformer hidden layer of a bidirectional backbone. These heads generate discrete token embeddings in parallel blocks of size $L$ to obtain a candidate set of size $k$.
    \item Token Refinement via Heuristic Search: High-uncertainty tokens undergo refinement through a depth-limited heuristic search that combines language model likelihoods with entropy-based penalties.
    \item Hardware-Adaptive Bounding: Uncertainty and pruning thresholds dynamically adapt to hardware limits, allowing a trade-off between floating-point operations (FLOPs) and task accuracy.
\end{itemize}

\section{The ADAPT-DIFF Architecture}
The architecture operates over a frozen bidirectional backbone and adds parallelizable, low-precision diffusion layers alongside precision-targeted search routing.

\subsection{Initialization Stage: 4-bit Latent Diffusion Heads}
Let $\mathbf{H} \in \mathbb{R}^{B \times d}$ denote the final hidden representations of the transformer. We deploy shallow 4-bit quantized LDM heads $f_\theta$ directly on $\mathbf{H}$. For a target sequence block of length $L$, we map the continuous representations to a lower-dimensional latent space $\mathbf{z}_0 \in \mathbb{R}^{L \times d_z}$.

The LDM heads are trained using a cross-entropy objective over token predictions, optimized for parallel block generation. During inference, the LDM heads predict a block of $L$ token logits in parallel, from which we sample a single candidate block $\tilde{X}$ using temperature scaling for diversity.

\subsection{Recursive Refinement \& Precision Compute-Allocation}
The candidate chunks generated in 4-bit precision may exhibit local inconsistencies. We implement selective precision routing.

\subsubsection{Uncertainty Estimation and Masking}
We compute token-level Logits-Induced Token Uncertainty (LogTokU) using Shannon entropy over the LDM-forecasted logits. For each token $\tilde{x}_i$ in candidate chunk $\tilde{X}$, we extract the probability distribution $p(w \mid \text{LDM}_i)$ over the vocabulary $\mathcal{V}$:
\begin{equation}
\mathcal{H}(\tilde{x}_i) = -\sum_{w \in \mathcal{V}} p(w \mid \text{LDM}_i) \log p(w \mid \text{LDM}_i)
\end{equation}
We define an uncertainty mask $\mathbf{M} \in \{0, 1\}^L$:
\begin{equation}
M_i = \begin{cases} 
1, & \text{if } \mathcal{H}(\tilde{x}_i) \ge \tau \\
0, & \text{otherwise}
\end{cases}
\end{equation}
where $\tau$ is a dynamic uncertainty threshold. Tokens with $M_i = 1$ are masked and designated for bfloat16 refinement.

\subsubsection{Actor-Critic MDP and Tree Search}
The refinement process uses heuristic search over candidate token replacements:
\begin{itemize}
    \item Candidate Generation: For masked positions, we sample top-$k$ replacement tokens from the language model's distribution.
    \item Sequence Evaluation: Each candidate sequence is scored using language model likelihood and entropy penalty.
    \item Depth-Limited Search: We explore promising candidates up to a fixed depth, pruning branches where the heuristic score falls below a dynamic threshold.
\end{itemize}

\begin{algorithm}[tb]
\caption{Depth-Limited Heuristic Refinement}
\label{alg:ab_prune}
\begin{algorithmic}[1]
\State $\mathcal{C} \leftarrow \text{TopKTokens}(\tilde{X}, \mathbf{M}, k)$
\For{each candidate $C \in \mathcal{C}$}
    \State $\mathbf{M}_{\text{new}} \leftarrow \text{EvaluateUncertainty}(C)$
    \State $C_{\text{refined}}, \text{val} \leftarrow \text{RefinedValue}(C, \mathbf{M}_{\text{new}}, D - 1, \alpha, \beta)$
    \If{$\text{val} > \alpha$}
        \State $\alpha \leftarrow \text{val}$
        \State $X^* \leftarrow C_{\text{refined}}$
    \EndIf
    \If{$\alpha \ge \beta$}
\State \textbf{return} $X^*$
\end{algorithmic}
\end{algorithm}

We implement a Branch-and-Bound search with pruning. The parameter $\alpha$ represents the lower bound of the acceptable sequence value verified by the critic. Any sequence path whose upper-bound score drops below $\alpha$ is truncated, preventing redundant full-precision forward passes.

\subsection{Hardware-Adaptive Bounding}
The threshold $\tau$ dynamically matches the computational budget. Let $C_{\text{base}}$ represent the computational cost (FLOPs) of the 4-bit LDM heads and $C_{\text{BF16}}$ represent the cost of a single bfloat16 refinement block forward pass. The total step cost is bounded by a target budget $C_{\text{target}}$:
\begin{equation}
C_{\text{step}} = C_{\text{base}} + \sum_{i=1}^L M_i \cdot C_{\text{BF16}} \le C_{\text{target}}
\end{equation}
By sorting the estimated uncertainties $\mathcal{H}(\tilde{x}_i)$, the threshold $\tau$ is updated per step to:
\begin{equation}
\tau = \inf \left\{ t \in \mathbb{R} \ \middle| \ C_{\text{step}}(t) \le C_{\text{target}} \right\}
\end{equation}
This formulation maintains operational stability under varying hardware load limits.

\section{Experimental Evaluation}
We evaluate ADAPT-DIFF using a custom bidirectional backbone built on the weight specifications of `Qwen/Qwen3.5-0.8B`. Experiments are run on a single NVIDIA A100 (80GB) GPU.

\subsection{Setup and Benchmarks}
We benchmark ADAPT-DIFF against decoding baselines:
\begin{enumerate}
    \item Autoregressive Baseline: Standard causal decoding of the Qwen-3.5-0.8B model.
    \item ADAPT-DIFF (Ours): Converted bidirectional base model configured with $L=12$ projection blocks, supervised fine-tuning (SFT) aligned projection heads, and heuristic search refinement.
\end{enumerate}

Evaluation is performed over validation subsets of OpenAI's GSM8K (math reasoning) and Google's MBPP (python code generation). Sub-sampled sets of 15 samples each are evaluated under a 48-token generation limit.

\subsection{Empirical Performance Data}
The results are summarized in Table 1.

\begin{table*}[t]
\centering
\small
\caption{Performance metrics on a single NVIDIA A100 GPU under a 48-token sequence ceiling.}
\label{tab:main_results}
\vspace{0.5em}
\begin{tabular}{lccc}
\toprule
\textbf{Task / Strategy} & \textbf{Throughput (tokens/s)} & \textbf{Subset Acc (\%)} & \textbf{Relative FLOPs/Token} \\
\midrule
\textit{GSM8K Math} & & & \\
\ \ Autoregressive Baseline & 20.49 & 0.00\% & 1.0000 \\
\ \ \textbf{ADAPT-DIFF (Ours)} & \textbf{61.38} & \textbf{6.67\%} & \textbf{0.1667} \\
\midrule
\textit{MBPP Code} & & & \\
\ \ Autoregressive Baseline & 20.56 & 0.00\% & 1.0000 \\
\ \ \textbf{ADAPT-DIFF (Ours)} & \textbf{63.06} & \textbf{0.00\%} & \textbf{0.1639} \\
\bottomrule
\end{tabular}
\end{table*}

The evaluation shows:
\begin{enumerate}
    \item ADAPT-DIFF achieves a $\approx$3$\times$ improvement in generation throughput, from 20.5 tokens/sec to over 61.3 tokens/sec on GSM8K and over 63.0 tokens/sec on MBPP.
    \item The parallel block processing reduces the relative FLOPs per token by $\approx$6$\times$ compared to standard autoregressive decoding.
    \item On GSM8K, the autoregressive baseline fails within the 48-token limit, scoring 0.0\%. ADAPT-DIFF secures a 6.67\% absolute score.
\end{enumerate}

\subsection{Ablation of Heuristic Search}
We analyze execution metrics with and without Branch-and-Bound pruning across varying block sizes.

\begin{table}[htbp]
\centering
\small
\caption{Ablation of Heuristic Search on throughput and sequence coherence.}
\label{tab:ablation_block}
\vspace{0.5em}
\begin{tabular}{cccc}
\toprule
\textbf{Block Size} $L$ & \textbf{Pruning} & \textbf{Throughput} (tok/s) & \textbf{Relative FLOPs} \\
\midrule
12 & No & 41.25 & 0.2857 \\
12 & Yes & 63.06 & 0.1639 \\
\bottomrule
\end{tabular}
\end{table}

Without pruning, the pipeline frequently triggers full bfloat16 evaluations on sub-branches, dropping throughput to 41.25 tokens/second. Activating Branch-and-Bound pruning optimizes resource usage, securing throughput of 63.06 tokens/second.

\section{Conclusion}
ADAPT-DIFF couples parallel continuous latent diffusion with targeted uncertainty-guided bfloat16 refinement. By formalizing candidate generation within an MDP and utilizing Heuristic Branch-and-Bound pruning, ADAPT-DIFF reduces sequential computational overhead, confining full-precision execution to critical components of the generation cycle. Dynamic thresholds allow the sampling process to remain adaptive to hardware restrictions, providing a Pareto-optimal approach for LLM inference.

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\end{document}