diff --git a/.github/workflows/CI.yml b/.github/workflows/CI.yml
index f7d43470e..4015ab331 100644
--- a/.github/workflows/CI.yml
+++ b/.github/workflows/CI.yml
@@ -4,9 +4,11 @@ on:
   push:
     branches:
       - master
+      - backport-*
   pull_request:
     branches:
       - master
+      - backport-*
   merge_group:
     types: [checks_requested]
 
diff --git a/Project.toml b/Project.toml
index eab8c362c..5dde3a427 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "DynamicPPL"
 uuid = "366bfd00-2699-11ea-058f-f148b4cae6d8"
-version = "0.30.1"
+version = "0.30.4"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
@@ -46,7 +46,7 @@ AbstractMCMC = "5"
 AbstractPPL = "0.8.4, 0.9"
 Accessors = "0.1"
 BangBang = "0.4.1"
-Bijectors = "0.13.18"
+Bijectors = "0.13.18, 0.14"
 ChainRulesCore = "1"
 Compat = "4"
 ConstructionBase = "1.5.4"
@@ -65,7 +65,7 @@ Requires = "1"
 ReverseDiff = "1"
 Test = "1.6"
 ZygoteRules = "0.2"
-julia = "~1.6.6, 1.7.3"
+julia = "1.10"
 
 [extras]
 ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
diff --git a/ext/DynamicPPLMCMCChainsExt.jl b/ext/DynamicPPLMCMCChainsExt.jl
index eb9745552..f950de6f1 100644
--- a/ext/DynamicPPLMCMCChainsExt.jl
+++ b/ext/DynamicPPLMCMCChainsExt.jl
@@ -108,86 +108,14 @@ function DynamicPPL.returned_quantities(
     varinfo = DynamicPPL.VarInfo(model)
     iters = Iterators.product(1:size(chain, 1), 1:size(chain, 3))
     return map(iters) do (sample_idx, chain_idx)
-        if DynamicPPL.supports_varname_indexing(chain)
-            varname_pairs = _varname_pairs_with_varname_indexing(
-                chain, varinfo, sample_idx, chain_idx
-            )
-        else
-            varname_pairs = _varname_pairs_without_varname_indexing(
-                chain, varinfo, sample_idx, chain_idx
-            )
-        end
-        fixed_model = DynamicPPL.fix(model, Dict(varname_pairs))
-        return fixed_model()
+        # TODO: Use `fix` once we've addressed https://github.com/TuringLang/DynamicPPL.jl/issues/702.
+        # Update the varinfo with the current sample and make variables not present in `chain`
+        # to be sampled.
+        DynamicPPL.setval_and_resample!(varinfo, chain, sample_idx, chain_idx)
+        # NOTE: Some of the varialbes can be a view into the `varinfo`, so we need to
+        # `deepcopy` the `varinfo` before passing it to the `model`.
+        model(deepcopy(varinfo))
     end
 end
 
-"""
-    _varname_pairs_with_varname_indexing(
-        chain::MCMCChains.Chains, varinfo, sample_idx, chain_idx
-    )
-
-Get pairs of `VarName => value` for all the variables in the `varinfo`, picking the values
-from the chain.
-
-This implementation assumes `chain` can be indexed using variable names, and is the
-preffered implementation.
-"""
-function _varname_pairs_with_varname_indexing(
-    chain::MCMCChains.Chains, varinfo, sample_idx, chain_idx
-)
-    vns = DynamicPPL.varnames(chain)
-    vn_parents = Iterators.map(vns) do vn
-        # The call nested_setindex_maybe! is used to handle cases where vn is not
-        # the variable name used in the model, but rather subsumed by one. Except
-        # for the subsumption part, this could be
-        # vn => getindex_varname(chain, sample_idx, vn, chain_idx)
-        # TODO(mhauru) This call to nested_setindex_maybe! is unintuitive.
-        DynamicPPL.nested_setindex_maybe!(
-            varinfo, DynamicPPL.getindex_varname(chain, sample_idx, vn, chain_idx), vn
-        )
-    end
-    varname_pairs = Iterators.map(Iterators.filter(!isnothing, vn_parents)) do vn_parent
-        vn_parent => varinfo[vn_parent]
-    end
-    return varname_pairs
-end
-
-"""
-Check which keys in `key_strings` are subsumed by `vn_string` and return the their values.
-
-The subsumption check is done with `DynamicPPL.subsumes_string`, which is quite weak, and
-won't catch all cases. We should get rid of this if we can.
-"""
-# TODO(mhauru) See docstring above.
-function _vcat_subsumed_values(vn_string, values, key_strings)
-    indices = findall(Base.Fix1(DynamicPPL.subsumes_string, vn_string), key_strings)
-    return !isempty(indices) ? reduce(vcat, values[indices]) : nothing
-end
-
-"""
-    _varname_pairs_without_varname_indexing(
-        chain::MCMCChains.Chains, varinfo, sample_idx, chain_idx
-    )
-
-Get pairs of `VarName => value` for all the variables in the `varinfo`, picking the values
-from the chain.
-
-This implementation does not assume that `chain` can be indexed using variable names. It is
-thus not guaranteed to work in cases where the variable names have complex subsumption
-patterns, such as if the model has a variable `x` but the chain stores `x.a[1]`.
-"""
-function _varname_pairs_without_varname_indexing(
-    chain::MCMCChains.Chains, varinfo, sample_idx, chain_idx
-)
-    values = chain.value[sample_idx, :, chain_idx]
-    keys = Base.keys(chain)
-    keys_strings = map(string, keys)
-    varname_pairs = [
-        vn => _vcat_subsumed_values(string(vn), values, keys_strings) for
-        vn in Base.keys(varinfo)
-    ]
-    return varname_pairs
-end
-
 end
diff --git a/src/utils.jl b/src/utils.jl
index bd5d365fc..5fedd3039 100644
--- a/src/utils.jl
+++ b/src/utils.jl
@@ -286,8 +286,15 @@ function (f::ReshapeTransform)(x)
     if size(x) != f.input_size
         throw(DimensionMismatch("Expected input of size $(f.input_size), got $(size(x))"))
     end
-    # The call to `tovec` is only needed in case `x` is a scalar.
-    return reshape(tovec(x), f.output_size)
+    if f.output_size == ()
+        # Specially handle the case where x is a singleton array, see
+        # https://github.com/JuliaDiff/ReverseDiff.jl/issues/265 and
+        # https://github.com/TuringLang/DynamicPPL.jl/issues/698
+        return fill(x[], ())
+    else
+        # The call to `tovec` is only needed in case `x` is a scalar.
+        return reshape(tovec(x), f.output_size)
+    end
 end
 
 function (inv_f::Bijectors.Inverse{<:ReshapeTransform})(x)
@@ -934,10 +941,10 @@ end
 """
     float_type_with_fallback(x)
 
-Return type corresponding to `float(typeof(x))` if possible; otherwise return `Real`.
+Return type corresponding to `float(typeof(x))` if possible; otherwise return `float(Real)`.
 """
-float_type_with_fallback(::Type) = Real
-float_type_with_fallback(::Type{Union{}}) = Real
+float_type_with_fallback(::Type) = float(Real)
+float_type_with_fallback(::Type{Union{}}) = float(Real)
 float_type_with_fallback(::Type{T}) where {T<:Real} = float(T)
 
 """
diff --git a/src/varinfo.jl b/src/varinfo.jl
index 11fe08d0f..4cf1f1b02 100644
--- a/src/varinfo.jl
+++ b/src/varinfo.jl
@@ -1694,6 +1694,8 @@ Return the current value(s) of the random variables sampled by `spl` in `vi`.
 
 The value(s) may or may not be transformed to Euclidean space.
 """
+getindex(vi::UntypedVarInfo, spl::Sampler) =
+    copy(getindex(vi.metadata.vals, _getranges(vi, spl)))
 getindex(vi::VarInfo, spl::Sampler) = copy(getindex_internal(vi, _getranges(vi, spl)))
 function getindex(vi::TypedVarInfo, spl::Sampler)
     # Gets the ranges as a NamedTuple
diff --git a/test/Project.toml b/test/Project.toml
index 36ee4baa8..36fcd1b69 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -31,7 +31,7 @@ ADTypes = "1"
 AbstractMCMC = "5"
 AbstractPPL = "0.8.4, 0.9"
 Accessors = "0.1"
-Bijectors = "0.13.9"
+Bijectors = "0.13.9, 0.14"
 Combinatorics = "1"
 Compat = "4.3.0"
 Distributions = "0.25"
diff --git a/test/turing/Project.toml b/test/turing/Project.toml
index 0dd3f20e0..28341c20b 100644
--- a/test/turing/Project.toml
+++ b/test/turing/Project.toml
@@ -15,5 +15,5 @@ DynamicPPL = "0.24, 0.25, 0.26, 0.27, 0.28, 0.29, 0.30"
 HypothesisTests = "0.11"
 MCMCChains = "6"
 ReverseDiff = "1.15"
-Turing = "0.33, 0.34"
+Turing = "0.33, 0.34, 0.35"
 julia = "1.7"
diff --git a/test/turing/varinfo.jl b/test/turing/varinfo.jl
index f1d805505..e5b8eb79f 100644
--- a/test/turing/varinfo.jl
+++ b/test/turing/varinfo.jl
@@ -342,4 +342,19 @@
         model = state_space(y, length(t))
         @test size(sample(model, NUTS(; adtype=AutoReverseDiff(true)), n), 1) == n
     end
+
+    if Threads.nthreads() > 1
+        @testset "DynamicPPL#684: OrderedDict with multiple types when multithreaded" begin
+            @model function f(x)
+                ns ~ filldist(Normal(0, 2.0), 3)
+                m ~ Uniform(0, 1)
+                return x ~ Normal(m, 1)
+            end
+            model = f(1)
+            chain = sample(model, NUTS(), MCMCThreads(), 10, 2)
+            loglikelihood(model, chain)
+            logprior(model, chain)
+            logjoint(model, chain)
+        end
+    end
 end