Stochasticity in discrete diffusion transitions induces error correction via redundant symmetric mass exchanges that provably contract sampling errors, enabling DCRS to improve speed-quality tradeoffs with fewer function evaluations on image and language tasks.
Strong data processing inequalities and $\Phi$-Sobolev inequalities for discrete channels
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
The noisiness of a channel can be measured by comparing suitable functionals of the input and output distributions. For instance, the worst-case ratio of output relative entropy to input relative entropy for all possible pairs of input distributions is bounded from above by unity, by the data processing theorem. However, for a fixed reference input distribution, this quantity may be strictly smaller than one, giving so-called strong data processing inequalities (SDPIs). The same considerations apply to an arbitrary $\Phi$-divergence. This paper presents a systematic study of optimal constants in SDPIs for discrete channels, including their variational characterizations, upper and lower bounds, structural results for channels on product probability spaces, and the relationship between SDPIs and so-called $\Phi$-Sobolev inequalities (another class of inequalities that can be used to quantify the noisiness of a channel by controlling entropy-like functionals of the input distribution by suitable measures of input-output correlation). Several applications to information theory, discrete probability, and statistical physics are discussed.
fields
cs.LG 1years
2026 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
On the Error-Correcting Effects of Stochasticity in Discrete Diffusion
Stochasticity in discrete diffusion transitions induces error correction via redundant symmetric mass exchanges that provably contract sampling errors, enabling DCRS to improve speed-quality tradeoffs with fewer function evaluations on image and language tasks.