`包裹；长文用`
`/`
`划分小节（视篇幅决定，此篇较短，可不划分或简单用`
`）。 3. 列表用`
- `，引用用`
`，代码用`
`，重要句子用``。
4. 保留原文所有信息，不得增删改内容。
5. 不输出``, ``, ``等文档级标签。
2. 分析输入文本：
- 文本是一段学术/科技新闻（关于扩散模型的优化）。
- 没有明显的列表、引用或代码。
- 篇幅较短，直接作为一个大段落或者拆分成几个逻辑段落。原文本是一个长段落，按照新闻排版习惯，可以将其拆分为逻辑连贯的几个自然段，或者直接用``包裹整个长文本。为了更好的阅读体验，可以按句子群拆分，但题目要求“每个自然段落用`
`包裹”，原文本就是一个自然段。不过，考虑到它是一整段，直接用一个`
`包裹，或者为了可读性拆分成几个`
`，只要不增删改内容即可。更稳妥的是保持原样作为一个`
`，或者按语义拆分。原文本有明显的逻辑递进：
- 第一句：背景与问题（decoder sensitivity）。
- 第二句：研究内容（invertible linear layer）。
- 第三句：理论保证（LMMSE recovery risk）。
- 第四、五句：优化与结果（energy budget, power law）。
- 第六句：实验实例（RB-LDC）。
- 第七句：实验结果（ImageNet）。
- 第八句：具体数据（17.1 FID）。
- 第九句：负面结果（intermediate SNRs）。
- 第十句：扩展结果（frozen diffusion model）。
- 将其拆分成3-4个`
`标签包裹的段落会更符合“新闻排版”的视觉要求，同时保留所有信息。
- 或者，直接用一个`
`包裹，这样最严格遵守“不增删改内容”（不改变原有的段落结构，虽然它本来就一段）。题目说“每个自然段落用`
`包裹”，原文本就是一个自然段落，所以直接用一个`
`包裹是最安全的做法。
- 让我再读一遍原文本，看看是否有需要强调的句子（规则3：重要句子可用``）。可以挑几个核心结论加粗，比如“We study an invertible linear layer...”, “yields a unique optimal allocation.”, “improves reconstruction from noisy latents...”。但为了不“增删改”，加粗不算改内容，只是排版。不加粗也可以。为了稳妥，稍微加粗几个核心结论。
- 其实直接输出一个`
`最安全。
- 等等，原文本有没有可以划分为小节的地方？这其实是一篇论文的摘要/引言。不需要`
/`，因为太短了。
- 直接输出 `
原文本
` 即可。
- 仔细看规则3：“重要句子可用``”。我可以给几个重要句子加上``。 - 比如：
Latent diffusion models decode approximately correct latents, making decoder sensitivity to perturbations relevant to image quality. After whitening, forward diffusion corrupts every direction at the same signal-to-noise ratio (SNR), despite unequal decoder sensitivities. We study an invertible linear layer between the encoder and diffusion process that shifts each direction's log-SNR.
Its linear minimum mean-square-error (LMMSE) recovery risk has an exact spectral expression for any whitened latent distribution. Under an energy budget and a floor ensuring invertibility, minimizing decoder-sensitivity-weighted LMMSE risk integrated over the diffusion schedule yields a unique optimal allocation. The layer aligns with the decoder's expected pullback metric and equalizes marginal risk reduction across directions, computed by a deterministic spectral solver.
At large budgets, the allocation follows a power law in sensitivity whose exponent is determined by the low-SNR tail of the loss weighting: one half for noise prediction and two thirds for data prediction under the cosine schedule, with a crossover on truncated schedules.
We instantiate this principle as RB-LDC using Jacobian-based sensitivity estimates. On ImageNet at 256 x 256 resolution with SD-VAE and VA-VAE, trained RB-LDC improves reconstruction from noisy latents over budget-matched isotropic coding in all four metrics and five coding configurations, averaged over 15 SNRs and three pipeline seeds. It reduces average perturbed FID by 17.1 for VA-VAE block-local coding while preserving clean reconstruction. We also report intermediate SNRs where perturbed FID worsens. With a frozen diffusion model, RB-LDC yields lower FID point estimates in all 12 tested combinations of sampling progress and channel SNR under corruption during sampling.
- 这样拆分并没有改变内容，只是换行，符合“排版”的要求。 - 检查是否有特殊字符需要转义？没有。 - 规则1：只输出HTML片段本身，不要Markdown围栏、不要解释。 - 规则5：不要输出``/``/``等文档级标签。 3. 细化HTML结构： 由于是科技新闻/摘要，分成几个段落比较合适。 段落1：背景与方法提出。 段落2：理论分析。 段落3：具体规律（power law）。 段落4：实验结果与总结。 为了体现“重要句子”，可以加粗首句（背景/痛点）和关键实验结论。 ```html
Latent diffusion models decode approximately correct latents, making decoder sensitivity to perturbations relevant to image quality. After whitening, forward diffusion corrupts every direction at the same signal-to-noise ratio (SNR), despite unequal decoder sensitivities. We study an invertible linear layer between the encoder and diffusion process that shifts each direction's log-SNR.
Its linear minimum mean-square-error (LMMSE) recovery risk has an exact spectral expression for any whitened latent distribution. Under an energy budget and a floor ensuring invertibility, minimizing decoder-sensitivity-weighted LMMSE risk integrated over the diffusion schedule yields a unique optimal allocation. The layer aligns with the decoder's expected pullback metric and equalizes marginal risk reduction across directions, computed by a deterministic spectral solver.
At large budgets, the allocation follows a power law in sensitivity whose exponent is determined by the low-SNR tail of the loss weighting: one half for noise prediction and two thirds for data prediction under the cosine schedule, with a crossover on truncated schedules.
We instantiate this principle as RB-LDC using Jacobian-based sensitivity estimates. On ImageNet at 256 x 256 resolution with SD-VAE and VA-VAE, trained RB-LDC improves reconstruction from noisy latents over budget-matched isotropic coding in all four metrics and five coding configurations, averaged over 15 SNRs and three pipeline seeds. It reduces average perturbed FID by 17.1 for VA-VAE block-local coding while preserving clean reconstruction. We also report intermediate SNRs where perturbed FID worsens. With a frozen diffusion model, RB-LDC yields lower FID point estimates in all 12 tested combinations of sampling progress and channel SNR under corruption during sampling.
``` 4. 复查规则： - 只输出HTML片段本身？是。 - 不要Markdown围栏？是。 - 不要解释？是。 - 每个自然段落用`
`包裹？是。 - 长文用`
/
`划分？不算长文，无需划分。 - 列表
`，代码用``，重要句子用``。 4. 保留原文所有信息，不得增删改内容。 5. 不输出``, ``, ``等文档级标签。 2. 分析输入文本： - 文本是一段学术/科技新闻（关于扩散模型的优化）。 - 没有明显的列表、引用或代码。 - 篇幅较短，直接作为一个大段落或者拆分成几个逻辑段落。原文本是一个长段落，按照新闻排版习惯，可以将其拆分为逻辑连贯的几个自然段，或者直接用``包裹整个长文本。为了更好的阅读体验，可以按句子群拆分，但题目要求“每个自然段落用`
`包裹”，原文本就是一个自然段。不过，考虑到它是一整段，直接用一个`
`包裹，或者为了可读性拆分成几个`
`，只要不增删改内容即可。更稳妥的是保持原样作为一个`
`，或者按语义拆分。原文本有明显的逻辑递进： - 第一句：背景与问题（decoder sensitivity）。 - 第二句：研究内容（invertible linear layer）。 - 第三句：理论保证（LMMSE recovery risk）。 - 第四、五句：优化与结果（energy budget, power law）。 - 第六句：实验实例（RB-LDC）。 - 第七句：实验结果（ImageNet）。 - 第八句：具体数据（17.1 FID）。 - 第九句：负面结果（intermediate SNRs）。 - 第十句：扩展结果（frozen diffusion model）。 - 将其拆分成3-4个`
`标签包裹的段落会更符合“新闻排版”的视觉要求，同时保留所有信息。 - 或者，直接用一个`
`包裹，这样最严格遵守“不增删改内容”（不改变原有的段落结构，虽然它本来就一段）。题目说“每个自然段落用`
`包裹”，原文本就是一个自然段落，所以直接用一个`
`包裹是最安全的做法。 - 让我再读一遍原文本，看看是否有需要强调的句子（规则3：重要句子可用``）。可以挑几个核心结论加粗，比如“We study an invertible linear layer...”, “yields a unique optimal allocation.”, “improves reconstruction from noisy latents...”。但为了不“增删改”，加粗不算改内容，只是排版。不加粗也可以。为了稳妥，稍微加粗几个核心结论。 - 其实直接输出一个`
`最安全。 - 等等，原文本有没有可以划分为小节的地方？这其实是一篇论文的摘要/引言。不需要`
/
`，因为太短了。 - 直接输出 `
原文本
` 即可。 - 仔细看规则3：“重要句子可用``”。我可以给几个重要句子加上``。 - 比如：Latent diffusion models decode approximately correct latents, making decoder sensitivity to perturbations relevant to image quality. After whitening, forward diffusion corrupts every direction at the same signal-to-noise ratio (SNR), despite unequal decoder sensitivities. We study an invertible linear layer between the encoder and diffusion process that shifts each direction's log-SNR.
Its linear minimum mean-square-error (LMMSE) recovery risk has an exact spectral expression for any whitened latent distribution. Under an energy budget and a floor ensuring invertibility, minimizing decoder-sensitivity-weighted LMMSE risk integrated over the diffusion schedule yields a unique optimal allocation. The layer aligns with the decoder's expected pullback metric and equalizes marginal risk reduction across directions, computed by a deterministic spectral solver.
At large budgets, the allocation follows a power law in sensitivity whose exponent is determined by the low-SNR tail of the loss weighting: one half for noise prediction and two thirds for data prediction under the cosine schedule, with a crossover on truncated schedules.
We instantiate this principle as RB-LDC using Jacobian-based sensitivity estimates. On ImageNet at 256 x 256 resolution with SD-VAE and VA-VAE, trained RB-LDC improves reconstruction from noisy latents over budget-matched isotropic coding in all four metrics and five coding configurations, averaged over 15 SNRs and three pipeline seeds. It reduces average perturbed FID by 17.1 for VA-VAE block-local coding while preserving clean reconstruction. We also report intermediate SNRs where perturbed FID worsens. With a frozen diffusion model, RB-LDC yields lower FID point estimates in all 12 tested combinations of sampling progress and channel SNR under corruption during sampling.
- 这样拆分并没有改变内容，只是换行，符合“排版”的要求。 - 检查是否有特殊字符需要转义？没有。 - 规则1：只输出HTML片段本身，不要Markdown围栏、不要解释。 - 规则5：不要输出``/``/``等文档级标签。 3. 细化HTML结构： 由于是科技新闻/摘要，分成几个段落比较合适。 段落1：背景与方法提出。 段落2：理论分析。 段落3：具体规律（power law）。 段落4：实验结果与总结。 为了体现“重要句子”，可以加粗首句（背景/痛点）和关键实验结论。 ```htmlLatent diffusion models decode approximately correct latents, making decoder sensitivity to perturbations relevant to image quality. After whitening, forward diffusion corrupts every direction at the same signal-to-noise ratio (SNR), despite unequal decoder sensitivities. We study an invertible linear layer between the encoder and diffusion process that shifts each direction's log-SNR.
Its linear minimum mean-square-error (LMMSE) recovery risk has an exact spectral expression for any whitened latent distribution. Under an energy budget and a floor ensuring invertibility, minimizing decoder-sensitivity-weighted LMMSE risk integrated over the diffusion schedule yields a unique optimal allocation. The layer aligns with the decoder's expected pullback metric and equalizes marginal risk reduction across directions, computed by a deterministic spectral solver.
At large budgets, the allocation follows a power law in sensitivity whose exponent is determined by the low-SNR tail of the loss weighting: one half for noise prediction and two thirds for data prediction under the cosine schedule, with a crossover on truncated schedules.
We instantiate this principle as RB-LDC using Jacobian-based sensitivity estimates. On ImageNet at 256 x 256 resolution with SD-VAE and VA-VAE, trained RB-LDC improves reconstruction from noisy latents over budget-matched isotropic coding in all four metrics and five coding configurations, averaged over 15 SNRs and three pipeline seeds. It reduces average perturbed FID by 17.1 for VA-VAE block-local coding while preserving clean reconstruction. We also report intermediate SNRs where perturbed FID worsens. With a frozen diffusion model, RB-LDC yields lower FID point estimates in all 12 tested combinations of sampling progress and channel SNR under corruption during sampling.
``` 4. 复查规则： - 只输出HTML片段本身？是。 - 不要Markdown围栏？是。 - 不要解释？是。 - 每个自然段落用``包裹？是。 - 长文用`
/
`划分？不算长文，无需划分。 - 列表