Are there any deterministic multi-block encryption constructions that have an avalanche effect going both ways?
I know no classical deterministic multi-blocks encryption construction with the desired avalanche property. And a serious problem is that any such construction, simply because it is deterministic, won't pass the formal definition of security under chosen plaintext, which CBC, CTR, CFB, OFB.. with random IV achieve.

So what's asked does not come with a precise definition of security. Given this, I can state anything without risk of contradiction from the standpoint of security. So here is something, essentially two passes of CBC encryption with IV the last block of the previous pass. For encryption:


Pad de message to an integer number of blocks; e.g.: append a single bit 1, then as few bit(s) 0 (possibly none) as strictly necessary to reach a multiple of the block size.
Let $b&gt;0$ be the number of blocks of padded plaintext $X$
If $b=1$, do $X_0\gets E(E(X_0))$ where $E$ is block encryption
Otherwise repeat for $i$ from $b$ to $3b-1$ (that is, $2b$ times):


$X_{i\bmod b}\gets E(X_{i-1\bmod b}\oplus X_{i\bmod b})$

Output ciphertext $X$


Decryption is:


Let $X$ be the ciphertext of exactly $b&gt;0$ blocks
If $b=1$, do $X_0\gets D(D(X_0))$ where $D$ is block decryption
Otherwise repeat for $i$ from $3b-1$ downto $b$ (that is, $2b$ times):


$X_{i\bmod b}\gets X_{i-1\bmod b}\oplus D(X_{i\bmod b})$

Remove padding; e.g.: while $X$ ends with a zero bit and is non-empty, remove the rightmost 0 bit; then if $X$ is non-empty, remove its last bit.
Output the plaintext $X$


We can improve diffusion in decryption by using PCBC rather than CBC, make the thing less malleable by throwing an extra $\oplus i$, do more passes, have an extra index hopping into $X$, derive a different key at each pass.. but without a definition of the security goal, that is moot.

Note: as pointed out elsewhere, plaintext changes do not propagate at all in CTR mode, contrary to the question's statement.