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\title[Clock Diffusion]{Clock Diffusion}
\subtitle{Efficient Semi-Autoregressive Continuous\newline Diffusion Language Models}
\author{Paper discussion: Schiff et al. (NVIDIA / Cornell)}
\date{arXiv:2610.00894v1 \quad $\cdot$ \quad 19 October 2026}

\begin{document}

\begin{frame}
  \titlepage
  \vspace{-0.7cm}
  \begin{center}
  \alert{Stagger denoising across tokens, then cache the finished prefix.}
  \end{center}
  \papersource{Reading presentation; not authored by the paper's authors.\quad
  \href{https://arxiv.org/abs/2610.00894v1}{arxiv.org/abs/2610.00894v1}}
\end{frame}

\begin{frame}{A continuous LM needs a prefix that stops changing}
  \begin{columns}[T]
    \begin{column}{0.48\textwidth}
      \begin{block}{Full-sequence diffusion}
      Repeatedly update all token latents.\par\medskip
      Dynamic future context prevents permanent prefix KV reuse.
      \end{block}
    \end{column}
    \begin{column}{0.48\textwidth}
      \begin{block}{Clock Diffusion}
      Give positions different noise schedules.\par\medskip
      Completed tokens become fixed context; an active window keeps denoising.
      \end{block}
    \end{column}
  \end{columns}
  \medskip
  \begin{itemize}
  \item Block clocks finish a group together; sliding clocks finish tokens in order.
  \item The contribution combines a probability model, training masks, and sampling.
  \end{itemize}
  \papersource{Paper, Secs. 1--3, PDF pp. 2--6; relationship to Rolling Diffusion: Sec. 5, p. 9.}
\end{frame}

\begin{frame}{Local clocks determine which positions need an update}
  \[
  u^\ell(t)=\clip\big(rt-\varphi(\ell)\big),
  \qquad r=1+\max_{\ell'}\varphi(\ell').
  \]
  \begin{itemize}
  \item Global time runs from $1$ to $0$ during generation.
  \item A larger phase $\varphi(\ell)$ makes a token finish earlier.
  \item For $s<t$, only $\A_{s\mid t}=\{\ell:u^\ell(s)<u^\ell(t)\}$ changes.
  \end{itemize}
  \begin{block}{A fixed clock means a fixed latent}
  $u^\ell(s)=u^\ell(t)$ implies a Dirac transition:
  $q(\z_s^\ell\mid\z_t^\ell,\x^\ell)=\delta(\z_s^\ell-\z_t^\ell)$.
  \end{block}
  \papersource{Paper, Sec. 3.1, Eqs. (2)--(9), PDF pp. 3--4.}
\end{frame}

\begin{frame}{Sliding clocks turn denoising into a pipeline}
  \[
  \varphi_{\mathrm{SW}}(\ell)=\frac{L-\ell}{S},\qquad
  u^\ell(t)=\clip\left(\frac{(L+S-1)t+\ell-L}{S}\right).
  \]
  \centering
  \includegraphics[width=0.98\linewidth,height=0.56\textheight,keepaspectratio]{figures/teaching-clock-ladder.pdf}
  \papersource{New teaching illustration from Eq. (11), PDF p. 5, and Appendix D, p. 25. $L$: length; $S$: window; $N$: updates/token.}
\end{frame}

\begin{frame}{ClockDLM predicts tokens and denoises their embeddings}
  \[
  \e^\ell=E^\top\x^\ell,\qquad
  \z_t^\ell\sim\mathcal N\!\left(\alpha(u^\ell(t))\e^\ell,
                 \sigma(u^\ell(t))^2I_d\right)
  \]
  \[
  \x_\theta^\ell\in\Delta^V
  \quad\longrightarrow\quad
  \e_\theta^\ell=E^\top\x_\theta^\ell
  \quad\longrightarrow\quad\text{Gaussian reverse update}
  \]
  \begin{itemize}
  \item Learned embedding matrix $E\in\R^{V\times d}$; $d=16$, unit-norm rows.
  \item The denoiser sees the active latents, local noise levels, and clean prefix.
  \item RePlaid components: learned schedule, self-conditioning, logit prior.
  \end{itemize}
  \papersource{Paper, Sec. 3.5 and Appendix B.1--B.4, PDF pp. 6, 18--21. Conditional-task sampling uses top-1 embeddings.}
\end{frame}

\begin{frame}{Causal clean states make permanent KV reuse valid}
  \begin{columns}[c]
    \begin{column}{0.43\textwidth}
    \includegraphics[width=\linewidth,height=0.68\textheight,keepaspectratio]{figures/fig02-training-mask.pdf}
    \end{column}
    \begin{column}{0.54\textwidth}
    \[
    \mathcal M=\begin{pmatrix}\mathcal M_{\mathrm{CC}}&0\\
      \mathcal M_{\mathrm{NC}}&\mathcal M_{\mathrm{NN}}\end{pmatrix}
    \]
    \begin{itemize}
    \item Training layout: clean $L$ tokens followed by noisy $L$ tokens.
    \item Noisy groups see their clean prefix and their own noisy group.
    \item Sliding windows remove the outlined clean-to-clean edges: token causality.
    \end{itemize}
    \end{column}
  \end{columns}
  \papersource{Paper, Fig. 2 and Sec. 3.3, PDF p. 5. Rows are queries; columns are keys.}
\end{frame}

\begin{frame}{One forward can write clean KV and denoise the window}
  \centering
  \includegraphics[width=0.93\linewidth,height=0.50\textheight,keepaspectratio]{figures/fig07-fused-cache.pdf}
  \begin{itemize}
  \item Concatenate newly committed tokens with the next active noisy window.
  \item Clean queries never see noisy keys: their cached states remain valid.
  \item Fuse caching with the next denoising pass to avoid an extra forward.
  \end{itemize}
  \papersource{Paper, Appendix D and Fig. 7, PDF p. 26. Existing KV forms the leftmost key group.}
\end{frame}

\begin{frame}{The likelihood bound charges only moving positions}
  \[
  -\log p_\theta(\x^{1:L})\le
  \mathcal L_{\mathrm{prior}}+\mathcal L_{\mathrm{recons}}
  +\mathcal L_{\mathrm{diffusion}}.
  \]
  \begin{itemize}
    \item Prior: terminal latent versus the Gaussian prior.
    \item Reconstruction: read out each token when it completes.
    \item Diffusion: reverse-transition KL over awake positions only.
  \end{itemize}
  \begin{block}{For Gaussian embedding diffusion}
  \[
  \KL_\ell=\frac12\big[\snr(u^\ell(s))-\snr(u^\ell(t))\big]
  \|\e^\ell-\e_\theta^\ell\|_2^2.
  \]
  \end{block}
  \papersource{Paper, Eq. (10), Appendix A and Eq. (23), PDF pp. 4, 17--19. Frozen positions have identical Dirac transitions.}
\end{frame}

\begin{frame}{Training proxies and likelihood evaluation use different clocks}
  \begin{columns}[T]
    \begin{column}{0.48\textwidth}
    \begin{block}{Efficient training}
    \begin{itemize}
    \item Draw independent times, then sort within each $S$-token group.
    \item Random gaps support variable-stride Cache Grab sampling.
    \item Reconstruction proxy: all noisy positions at $u=0$.
    \end{itemize}
    \end{block}
    \end{column}
    \begin{column}{0.48\textwidth}
    \begin{block}{PPL evaluation}
    \begin{itemize}
    \item Randomly shift the group partition and attention mask.
    \item Restore time gaps of $1/S$.
    \item Estimate reconstruction and diffusion separately and without bias.
    \end{itemize}
    \end{block}
    \end{column}
  \end{columns}
  \medskip
  \alert{The cleaner-context reconstruction proxy is not itself a valid likelihood bound.}
  \papersource{Paper, Appendix C.2, Algorithms 2--3 and Eqs. (49)--(52), PDF pp. 24--25.}
\end{frame}

\begin{frame}{Confidence commits the longest eligible prefix}
  A token is eligible when its budget expires \textbf{or} its top-token probability
  reaches a threshold $\eta<1$.
  \medskip
  \begin{center}
  \begin{tabular}{lrrrr}
  \toprule
  Window position & 1 & 2 & 3 & 4\\
  \midrule
  Top probability & 0.98 & 0.96 & 0.70 & 0.99\\
  Commit at $\eta=0.95$ & yes & yes & no & no\\
  \bottomrule
  \end{tabular}
  \end{center}
  \begin{itemize}
  \item The example assumes that no token has exhausted its budget.
  \item Keep the remaining latents and ages; refill on the right.
  \item No retraining required. A block model must wait for the whole block.
  \end{itemize}
  \papersource{Teaching example of Algorithms 4--5, Appendix E.1, PDF pp. 26--27. $\eta=1$ disables confidence commits.}
\end{frame}

\begin{frame}{SSD verifies drafts and keeps unfinished continuous states}
  \centering
  \includegraphics[width=0.94\linewidth,height=0.32\textheight,keepaspectratio]{figures/fig03-cache-grab.pdf}
  \begin{itemize}
  \item Retrain with joint AR + diffusion loss; share model parameters.
  \item Two calls per iteration: diffusion draft, then causal AR verification.
  \item Accept the matching prefix plus the AR correction at the first mismatch.
  \item Retain the uncommitted tail; reaching $u=0$ does not force a commit.
  \end{itemize}
  \papersource{Paper, Fig. 3 (right), Appendix E.2 and F, PDF pp. 6, 27--28. Top-1 output matches this joint model's AR decoding.}
\end{frame}

\begin{frame}{A sliding window does not automatically reduce call count}
  \[
  T_{\mathrm{block}}=\frac{L}{S}N,\qquad
  T_{\mathrm{SW}}=\frac{L+S-1}{S}N.
  \]
  \begin{itemize}
  \item At $N=S$, the standard sliding sampler takes $L+S-1$ denoising calls.
  \item It commits one token per call after the pipeline fills.
  \item Lower budgets use cohorts; Cache Grab skips work by early commits.
  \end{itemize}
  \begin{block}{How to interpret efficiency}
  NFE counts all forwards, including setup and SSD verification.\par
  It does not measure latency: the tokens and attention work per call differ.
  \end{block}
  \papersource{Paper, Appendix D, PDF pp. 25--26; NFE accounting in Appendix F, p. 28. Fixed-length formulas exclude setup overhead.}
\end{frame}

\begin{frame}{Three tasks test different consequences of the design}
  \begin{center}
  \begin{tabular}{@{}llll@{}}
  \toprule
  Training data & Evaluation & Updates & Main metric\\
  \midrule
  OpenWebText & 100k held-out docs & 1M & PPL bound $\downarrow$\\
  TinyGSM & GSM8K, 1,319 tasks & 250k & pass@1 $\uparrow$\\
  CNN/DailyMail & 11,490 test articles & up to 500k & ROUGE $\uparrow$\\
  \bottomrule
  \end{tabular}
  \end{center}
  \begin{itemize}
  \item OWT / math: 12-layer DiT, width 768, 12 attention heads.
  \item Summarization: Qwen3-style architecture, trained from scratch.
  \item GSM8K is evaluated by executing generated Python programs.
  \item Generation: seed 1, batch 1 per GPU; NFE SD is across examples.
  \end{itemize}
  \papersource{Paper, Appendix F and Tables 4--6, PDF pp. 28--32. Tokenizer names do not imply pretrained model weights.}
\end{frame}

\begin{frame}{OWT: 19.5 is the best reported diffusion PPL bound}
  \begin{columns}[c]
  \begin{column}{0.52\textwidth}
  \begin{tabular}{@{}lrr@{}}
  \toprule
  Model & $S$ & PPL $\downarrow$\\
  \midrule
  AR & --- & 17.5\\
  RePlaid & full & 21.3\\
  BD3LM & 16 & 22.3\\
  BD3LM & 4 & 20.7\\
  B-ClockDLM & 4 & 20.2\\
  ClockDLM & 16 & 20.6\\
  ClockDLM & 4 & \textbf{19.5}\\
  \bottomrule
  \end{tabular}
  \end{column}
  \begin{column}{0.44\textwidth}
  \begin{block}{The ``38\%'' claim}
  AR gap: $3.2\to2.0$.\par\medskip
  $(3.2-2.0)/3.2=37.5\%$.
  \end{block}
  The PPL reduction versus BD3LM itself is about 5.8\%.
  \medskip
  Diffusion values are variational upper bounds; AR is ordinary PPL.
  \end{column}
  \end{columns}
  \papersource{Paper, Table 1, PDF p. 7. Some baseline values are taken from prior work; RePlaid is retrained.}
\end{frame}

\begin{frame}{GSM8K: quality and call savings come in distinct stages}
  \begin{center}
  \begin{tabular}{@{}lrr@{}}
  \toprule
  Model / sampler & Mean NFE $\downarrow$ & pass@1 $\uparrow$\\
  \midrule
  AR baseline & 158.4 & 64.3\%\\
  RePlaid & 1025.0 & 44.5\%\\
  BD3LM, $S=32$ & 177.7 & 61.8\%\\
  B-ClockDLM, $S=32$ & 190.1 & 54.3\%\\
  ClockDLM, $S=32$ & 188.1 & 59.6\%\\
  \quad + Confidence, $\eta=0.7$ & 59.5 & 60.0\%\\
  \quad + SSD, joint training & \textbf{35.5} & \textbf{67.6\%}\\
  \bottomrule
  \end{tabular}
  \end{center}
  \medskip
  Confidence: $3.16\times$ fewer calls than standard ClockDLM.\par
  SSD: $4.46\times$ fewer calls and $+3.3$ accuracy points versus the AR baseline.
  \papersource{Paper, Tables 2 and 7, PDF pp. 7, 33. Clock models use $N=S$; SSD requires a separately trained joint model.}
\end{frame}

\begin{frame}{The sliding model improves the math budget frontier}
  \centering
  \includegraphics[width=0.98\linewidth,height=0.59\textheight,keepaspectratio]{figures/fig04-gsm-pareto.pdf}
  \begin{itemize}
  \item Compare points toward the upper left: higher accuracy, fewer calls.
  \item Standard $S=32$ ClockDLM is below BD3LM at the main-table budget;
        several smaller budgets favor the sliding model.
  \end{itemize}
  \papersource{Paper, Fig. 4, PDF p. 8. Log-scale NFE axis. Clock models sweep $N$; SW-SetDLM sweeps a confidence threshold.}
\end{frame}

\begin{frame}{Confidence saves calls, with task-dependent quality costs}
  \begin{center}
  \begin{tabular}{@{}llrr@{}}
  \toprule
  Model & $S$ & Standard: NFE / Acc. & $\eta=0.7$: NFE / Acc.\\
  \midrule
  ClockDLM & 32 & 188.1 / 59.6\% & 59.5 / 60.0\%\\
  ClockDLM & 64 & 219.1 / 55.6\% & 78.4 / 53.6\%\\
  B-ClockDLM & 32 & 190.1 / 54.3\% & 71.1 / 53.4\%\\
  B-ClockDLM & 64 & 220.1 / 49.1\% & 103.6 / 48.4\%\\
  \bottomrule
  \end{tabular}
  \end{center}
  \begin{itemize}
  \item A sliding model can commit a prefix; a block model waits for all positions.
  \item Lower thresholds reduce calls, but GSM8K accuracy is not monotonic.
  \item At $S=64$, the sliding model loses 2.0 accuracy points at $\eta=0.7$.
  \end{itemize}
  \papersource{Paper, Appendix G.2 and Table 7, PDF pp. 32--33. $N=S$; NFE means shown.}
\end{frame}

\begin{frame}{Joint training helps even when SSD is not used}
  \begin{center}
  \begin{tabular}{@{}rrrr@{}}
  \toprule
  Window $S$ & Diffusion loss only & Joint AR + diffusion & Change\\
  \midrule
  4 & 65.7\% & 66.6\% & +0.9 pp\\
  8 & 63.8\% & 67.2\% & +3.4 pp\\
  16 & 60.0\% & 63.8\% & +3.8 pp\\
  32 & 59.6\% & 63.5\% & +3.9 pp\\
  64 & 55.6\% & 61.3\% & +5.7 pp\\
  \bottomrule
  \end{tabular}
  \end{center}
  \begin{block}{Both columns use standard diffusion decoding}
  NFE is essentially unchanged. At $S=32$: 188.1 versus 187.4.\par
  The main-table SSD gain therefore includes a training effect.
  \end{block}
  \papersource{Paper, Table 8, PDF p. 33. Accuracy on all 1,319 GSM8K test examples. pp = percentage points.}
\end{frame}

\begin{frame}{Summarization still trails discrete diffusion}
  \begin{center}
  \begin{tabular}{@{}lrrrr@{}}
  \toprule
  Model & NFE & R-1 & R-2 & R-L\\
  \midrule
  AR & 73.1 & 35.9 & 14.8 & 25.0\\
  BD3LM, $S=32$ & 110.7 & 39.4 & 17.5 & 27.0\\
  SW-SetDLM, $S\le64$ & 72.2 & 39.7 & 17.9 & 27.8\\
  RePlaid, $T=1024$ & 1025.0 & 32.2 & 12.7 & 22.1\\
  ClockDLM, $S=32$ & 120.3 & 36.0 & 14.1 & 23.8\\
  \bottomrule
  \end{tabular}
  \end{center}
  \begin{itemize}
  \item Versus RePlaid: all three ROUGE scores improve; $8.52\times$ fewer calls.
  \item Discrete models offer better quality at similar or lower call counts.
  \item ROUGE does not directly measure factual accuracy.
  \end{itemize}
  \papersource{Paper, Table 3, PDF p. 8; protocol in Appendix F.3, pp. 30--32. All models trained from scratch; NFE means shown.}
\end{frame}

\begin{frame}{Open-ended generation exposes a low-budget failure region}
  \begin{columns}[c]
  \begin{column}{0.48\textwidth}
    \includegraphics[width=\linewidth,height=0.65\textheight,keepaspectratio]{figures/fig08-owt-mauve.pdf}
  \end{column}
  \begin{column}{0.48\textwidth}
    \begin{itemize}
    \item ClockDLM is stronger around 512+ calls.
    \item At roughly 64--256 calls, its MAUVE is near zero.
    \item At a total budget near 256: about 16 updates/token for ClockDLM,
          versus 256 for full-sequence RePlaid.
    \end{itemize}
  \end{column}
  \end{columns}
  \papersource{Paper, Appendix G.1 and Fig. 8, PDF pp. 31--32. $S=64$; 5,120 sequences; each model uses its best tested filtering settings.}
\end{frame}

\begin{frame}{The main lesson is to co-design clocks and dependencies}
  \begin{enumerate}
  \item \textbf{Representation:} continuous embedding diffusion can support
        variable-length generation and a stable prefix KV cache.
  \medskip
  \item \textbf{Computation:} prefix commits save calls; Confidence preserves
        the existing diffusion weights, while SSD adds joint AR training and verification.
  \medskip
  \item \textbf{Evidence:} OWT likelihood and math improve, while summarization
        and low-budget open generation remain concrete weaknesses.
  \end{enumerate}
  \medskip
  \alert{Next tests: closer training/commit-time alignment, larger models,
  and measured serving latency.}
  \papersource{Synthesis from Sec. 6, Tables 1--3, Appendix C.2 and Fig. 8. Proposed tests are discussion points.}
\end{frame}

\begin{frame}{Paper reference and discussion}
  \textbf{Clock Diffusion: Efficient Semi-Autoregressive Continuous Diffusion Language Models}
  \medskip
  \par Yair Schiff, Omer Belhasin, Roy Uziel, Matan Rusanovsky, Ran Zilberstein,
  Marianne Arriola, Gilad Turok, Guanghan Wang, Volodymyr Kuleshov, Michael Elad.
  \medskip
  \par NVIDIA and Cornell University. arXiv:2610.00894v1, 1 October 2026.
  \par\href{https://arxiv.org/abs/2610.00894v1}{https://arxiv.org/abs/2610.00894v1}
  \begin{block}{Discussion question}
  At a fixed latency budget, how should a sampler allocate window width,
  per-token denoising depth, and early-commit confidence?
  \end{block}
  \papersource{Main talk ends here (approximately 25 minutes). Backup slides contain derivations and additional protocol details.}
\end{frame}

\appendix

\begin{frame}{Backup: completion is a boundary with noisy future context}
  \[
  \tau_\ell=\frac{L-\ell}{L+S-1},\qquad
  \A_{\tau_\ell^+}=\{\ell,\ldots,\min(\ell+S-1,L)\}.
  \]
  \[
  u^j(\tau_\ell)=\frac{j-\ell}{S},\qquad
  \C_{\tau_\ell^+}=\{1,\ldots,\ell-1\}.
  \]
  \[
  \mathcal L_{\mathrm{recons}}^{\infty,\mathrm{SW}}
  =\sum_{\ell=1}^L\E_q\left[-\log p_\theta\!
  \left(\x^\ell\mid\z_{\tau_\ell}^{\A_{\tau_\ell^+}},\x^{<\ell}\right)\right].
  \]
  \begin{itemize}
  \item At $S=4$, the completion ladder is $[0,1/4,1/2,3/4]$.
  \item Each reconstruction target has a different window and clean prefix.
  \end{itemize}
  \papersource{Paper, Appendix B.6, Eqs. (41)--(44), PDF pp. 22--23.}
\end{frame}

\begin{frame}{Backup: unbiased validation uses shifted windows}
  Choose $\rho\sim\mathrm{Uniform}\{0,\ldots,S-1\}$; shift groups and mask.
  Let $j(\ell)=(\ell-\rho)\bmod S$.
  \begin{block}{Reconstruction}
  \[
  u^\ell=\frac{j(\ell)}S,\qquad
  \widehat{\mathcal L}_{\mathrm{recons}}
  =S\sum_\ell\mathbf1[j(\ell)=0]\cdot\mathrm{CE}_\ell.
  \]
  CE is token cross-entropy; each token is a head with probability $1/S$.
  \end{block}
  \begin{block}{Diffusion}
  \[
  u^\ell=\frac{j(\ell)+U}{S},\qquad U\sim\mathrm{Uniform}[0,1]\ \text{per group}.
  \]
  Random position offsets make each token's local time uniform on $[0,1]$.
  \end{block}
  \papersource{Paper, Appendix C.2, Eqs. (50)--(52), PDF p. 25. Validation: four forwards/batch with self-conditioning.}
\end{frame}

\begin{frame}{Backup: the continuous-time loss includes a clock derivative}
  \[
  \mathcal L_{\mathrm{diffusion}}^\infty
  =\int_0^1\E_q\!\left[
  \sum_{\ell\in\A_{t^+}}
  -\frac12\snr'(u^\ell(t))\dot u^\ell(t)
  \|\e^\ell-\e_\theta^\ell\|_2^2
  \right]dt.
  \]
  \begin{itemize}
  \item $\snr(u)=\alpha(u)^2/\sigma(u)^2$ decreases as forward noise grows.
  \item For sliding clocks, $\dot u^\ell=(L+S-1)/S$ while a position is awake.
  \item Under $du=\dot u^\ell(t)dt$, the clock derivative cancels the measure change.
  \end{itemize}
  \medskip
  Assumptions: absolutely continuous clocks and a continuously differentiable
  base SNR schedule (derivatives almost everywhere).
  \papersource{Paper, Eq. (27), PDF p. 19; Eqs. (45)--(48), p. 23. Denoiser conditioning is suppressed in the display.}
\end{frame}

\begin{frame}{Backup: a learned residual corrects an analytic token prior}
  With unit-norm embedding rows, the Gaussian log-likelihood gives
  \[
  \pi_t^\ell=\frac{\alpha(u^\ell(t))}{\sigma(u^\ell(t))^2}E\z_t^\ell.
  \]
  The final vocabulary probabilities are
  \[
  \x_\theta^\ell=\softmax\left(
  30\tanh\!\left(\frac{h_\theta^\ell}{30}\right)+\pi_t^\ell\right).
  \]
  \begin{itemize}
  \item $h_\theta^\ell$ is the learned vocabulary-logit vector.
  \item Soft-capping applies to the learned logits, not to the analytic prior.
  \item Input rescaling and self-conditioning stabilize the 16-dimensional latents.
  \end{itemize}
  \papersource{Paper, Appendix B.4, Eqs. (31)--(32), PDF p. 21. Noise schedules and optimizer settings vary by task.}
\end{frame}

\begin{frame}{Backup: summarization confidence gains are modest}
  \begin{columns}[c]
  \begin{column}{0.45\textwidth}
  \includegraphics[width=\linewidth,height=0.67\textheight,keepaspectratio]{figures/fig06-summary-confidence.pdf}
  \end{column}
  \begin{column}{0.51\textwidth}
  \begin{itemize}
  \item Hollow points: standard decoding.
  \item Lower threshold: fewer calls, generally lower ROUGE-1.
  \item From $\eta=0.99$ to $0.7$: about $1.1$--$1.2\times$ fewer calls;
        at most 1.3\% relative ROUGE-1 reduction.
  \item The threshold comparison starts at 0.99, not at the hollow points.
  \end{itemize}
  \end{column}
  \end{columns}
  \papersource{Paper, Sec. 4.3 and Fig. 6, PDF pp. 8--9. Green: $S=32$; blue: $S=64$.}
\end{frame}

\begin{frame}{Backup: conditional-task protocols differ in meaningful ways}
  \begin{columns}[T]
  \begin{column}{0.48\textwidth}
    \begin{block}{TinyGSM $\to$ GSM8K}
    \begin{itemize}
    \item Code continuation, context 512.
    \item Padding contributes to diffusion-model loss.
    \item Execute the generated program; tolerance $10^{-3}$.
    \item Fixed 250k-step EMA checkpoint.
    \end{itemize}
    \end{block}
  \end{column}
  \begin{column}{0.48\textwidth}
    \begin{block}{CNN/DailyMail}
    \begin{itemize}
    \item Article 512 tokens; target 180; canvas 768.
    \item Padding excluded from loss and attention.
    \item Minimum 50 generated non-EOS tokens; length/repetition penalties.
    \item Best validation-loss checkpoint.
    \end{itemize}
    \end{block}
  \end{column}
  \end{columns}
  \papersource{Paper, Appendix F.2--F.3 and Tables 5--6, PDF pp. 29--32. Both use DDPM with top-1 clean-token estimates.}
\end{frame}

\end{document}